<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2023000200015</article-id>
<article-id pub-id-type="doi">10.31349/revmexfis.69.021401</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Extended Jacobi elliptic function solutions for general boussinesq systems]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[San]]></surname>
<given-names><![CDATA[Sait]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Altunay]]></surname>
<given-names><![CDATA[Rabia]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Eski&#351;ehir Osmangazi University Department of Mathematics-Computer ]]></institution>
<addr-line><![CDATA[Eski&#351;ehir ]]></addr-line>
<country>Turkey</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>04</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>04</month>
<year>2023</year>
</pub-date>
<volume>69</volume>
<numero>2</numero>
<fpage>0</fpage>
<lpage>0</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2023000200015&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2023000200015&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2023000200015&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this research paper, we have utilized the Jacobi elliptic function expansion method to obtain the exact solutions of (1+1)- dimensional Boussinesq System (GBQS). The most important difference that distinguishes this method from other methods is the parameters included in the auxiliary equation    F  ' ( &#958; ) =  P   F  4 ( &#958; ) + Q   F  2 ( &#958; ) + R. As far as the authors know, there is no other study in which such a variety of solutions has been given. Depending on  P,  Q and  R, nineteen the solitary wave and periodic wave solutions are obtained at their limit conditions. In addition, 3D and contour plot graphics for the constructed waves are investigated with the computer package program by giving special values to the parameters involved. The validity and reliability of the method is examined by its applications on a class of nonlinear evolution equations of special interest in nonlinear mathematical physics. The results were acquired to verify that the recommended method is applicable and reliable for the analytic treatment of a wide application of nonlinear phenomena.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Jacobi elliptic function method]]></kwd>
<kwd lng="en"><![CDATA[travelling wave solution]]></kwd>
<kwd lng="en"><![CDATA[boussinesq system]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zhang J]]></surname>
<given-names><![CDATA[E]]></given-names>
</name>
<name>
<surname><![CDATA[Chen C]]></surname>
<given-names><![CDATA[L]]></given-names>
</name>
<name>
<surname><![CDATA[Li Y]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On Boussinesq models of constant depth]]></article-title>
<source><![CDATA[Phys Fluids]]></source>
<year>2004</year>
<volume>16</volume>
<page-range>1287</page-range></nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chen C]]></surname>
<given-names><![CDATA[L]]></given-names>
</name>
<name>
<surname><![CDATA[Lou S]]></surname>
<given-names><![CDATA[Y]]></given-names>
</name>
<name>
<surname><![CDATA[Li Y]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Solitary wave solutions for a general Boussinesq type fluid model]]></article-title>
<source><![CDATA[CommuniNonlinear Sci Numer Simul]]></source>
<year>2004</year>
<volume>9</volume>
<page-range>583</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bona]]></surname>
<given-names><![CDATA[J.L.]]></given-names>
</name>
<name>
<surname><![CDATA[Chen]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Saut]]></surname>
<given-names><![CDATA[J.-C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. II: The nonlinear theory]]></article-title>
<source><![CDATA[Nonlinearity]]></source>
<year>2004</year>
<volume>17</volume>
<page-range>925</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kaup]]></surname>
<given-names><![CDATA[D.J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A higher-order wave equation and the method for solving it]]></article-title>
<source><![CDATA[Prog. Theor. Phys.]]></source>
<year>1975</year>
<volume>54</volume>
<page-range>396</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tchier]]></surname>
<given-names><![CDATA[Fairouz]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Time fractional third-order variant Boussinesq system: Symmetry analysis, explicit solutions, conservation laws and numerical approximations]]></article-title>
<source><![CDATA[The European Physical Journal Plus]]></source>
<year>2018</year>
<volume>133</volume>
<page-range>240</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Meng]]></surname>
<given-names><![CDATA[De-Xin]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Solitonic solutions for a variable-coefficient variant Boussinesq system in the long gravity waves]]></article-title>
<source><![CDATA[Applied Mathematics and Computation]]></source>
<year>2009</year>
<volume>215</volume>
<page-range>1744</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ya&#351;ar]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Giresunlu]]></surname>
<given-names><![CDATA[I. B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Lie symmetry reductions, exact solutions and conservation laws of the third order variant Boussinesq system]]></article-title>
<source><![CDATA[Acta Physica Polonica A]]></source>
<year>2015</year>
<volume>128</volume>
<page-range>252</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zhang]]></surname>
<given-names><![CDATA[Jin E.]]></given-names>
</name>
<name>
<surname><![CDATA[Chen]]></surname>
<given-names><![CDATA[Chunli]]></given-names>
</name>
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[Yishen]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On Boussinesq models of constant depth]]></article-title>
<source><![CDATA[Physics of Fluids]]></source>
<year>2004</year>
<volume>16</volume>
<page-range>1287</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[JiBin]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Bifurcations of travelling wave solutions for two generalized Boussinesq systems]]></article-title>
<source><![CDATA[Science in China Series A: Mathematics]]></source>
<year>2008</year>
<volume>51</volume>
<page-range>1577</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Shou-Jun]]></surname>
<given-names><![CDATA[Huang]]></given-names>
</name>
<name>
<surname><![CDATA[Chun-Li]]></surname>
<given-names><![CDATA[Chen]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Study on solitary waves of a general Boussinesq model]]></article-title>
<source><![CDATA[Communications in Theoretical Physics]]></source>
<year>2007</year>
<volume>48</volume>
<page-range>773</page-range></nlm-citation>
</ref>
<ref id="B11">
<label>11</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chen]]></surname>
<given-names><![CDATA[Chunli]]></given-names>
</name>
<name>
<surname><![CDATA[Huang]]></surname>
<given-names><![CDATA[Shoujun]]></given-names>
</name>
<name>
<surname><![CDATA[Jin]]></surname>
<given-names><![CDATA[E. Zhang]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On head-on collisions between two solitary waves of Nwogu&#8217;s Boussinesq model]]></article-title>
<source><![CDATA[Journal of the Physical Society of Japan]]></source>
<year>2008</year>
<volume>77</volume>
</nlm-citation>
</ref>
<ref id="B12">
<label>12</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[San]]></surname>
<given-names><![CDATA[Sait]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Invariant analysis of nonlinear time fractional Qiao equation]]></article-title>
<source><![CDATA[Nonlinear Dynamics]]></source>
<year>2016</year>
<volume>85</volume>
<page-range>2127</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>13</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ya&#351;ar]]></surname>
<given-names><![CDATA[Emrullah]]></given-names>
</name>
<name>
<surname><![CDATA[San]]></surname>
<given-names><![CDATA[Sait]]></given-names>
</name>
<name>
<surname><![CDATA[Özkan]]></surname>
<given-names><![CDATA[Ye&#351;im Sa&#287;lam]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation]]></article-title>
<source><![CDATA[Open Physics]]></source>
<year>2016</year>
<volume>14</volume>
<page-range>37</page-range></nlm-citation>
</ref>
<ref id="B14">
<label>14</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[San]]></surname>
<given-names><![CDATA[Sait]]></given-names>
</name>
<name>
<surname><![CDATA[Ya&#351;ar]]></surname>
<given-names><![CDATA[Emrullah]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the conservation laws of Derrida-Lebowitz-Speer-Spohn equation]]></article-title>
<source><![CDATA[Communications in Nonlinear Science and Numerical Simulation]]></source>
<year>2015</year>
<volume>22</volume>
<page-range>1297</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>15</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Y. Wu]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Long waves in ocean and coastal waves]]></article-title>
<source><![CDATA[J. Eng. Mech.]]></source>
<year>1981</year>
<volume>107</volume>
<page-range>501</page-range></nlm-citation>
</ref>
<ref id="B16">
<label>16</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nwogu]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An alternative form of the Boussinesq equations for nearshorewave propagation]]></article-title>
<source><![CDATA[J. Waterw., Port, Coastal, Ocean Eng]]></source>
<year>1993</year>
<volume>119</volume>
<page-range>618</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>17</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tang]]></surname>
<given-names><![CDATA[Bo]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A generalized fractional sub-equation method for fractional differential equations with variable coefficients]]></article-title>
<source><![CDATA[Physics Letters A]]></source>
<year>2012</year>
<volume>376</volume>
<page-range>2588</page-range></nlm-citation>
</ref>
<ref id="B18">
<label>18</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bulut]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Yusuf]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Modified trial equation method to the nonlinear fractional Sharma-Tasso-Olever equation]]></article-title>
<source><![CDATA[International Journal of Modeling and Optimization]]></source>
<year>2013</year>
<volume>3</volume>
<page-range>353</page-range></nlm-citation>
</ref>
<ref id="B19">
<label>19</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Taghizadeh]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Application of the simplest equation method to some time-fractional partial differential equations]]></article-title>
<source><![CDATA[Ain Shams Engineering Journal]]></source>
<year>2013</year>
<volume>4</volume>
<page-range>897</page-range></nlm-citation>
</ref>
<ref id="B20">
<label>20</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tuluce Demiray]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Yusuf]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Hasan]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Generalized Kudryashov method for time-fractional differential equations]]></article-title>
<source><![CDATA[Abstract and applied analysis]]></source>
<year>2014</year>
<volume>2014</volume>
</nlm-citation>
</ref>
<ref id="B21">
<label>21</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bulut]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Yusuf]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Tuluce Demiray]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Exact solutions of time-fractional KdV equations by using generalized Kudryashov method]]></article-title>
<source><![CDATA[International Journal of Modeling and Optimization]]></source>
<year>2014</year>
<volume>4</volume>
<page-range>315</page-range></nlm-citation>
</ref>
<ref id="B22">
<label>22</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ya&#351;ar]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Y&#305;ld&#305;r&#305;m]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Masood Khalique]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Lie symmetry analysis, conservation laws and exact solutions of the seventh-order time fractional Sawada-Kotera-Ito equation]]></article-title>
<source><![CDATA[Results in physics]]></source>
<year>2016</year>
<volume>6</volume>
<page-range>322</page-range></nlm-citation>
</ref>
<ref id="B23">
<label>23</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fu]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations]]></article-title>
<source><![CDATA[Physics Letters A]]></source>
<year>2001</year>
<volume>290</volume>
<page-range>72</page-range></nlm-citation>
</ref>
<ref id="B24">
<label>24</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Yan]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Abundant families of Jacobi elliptic function solutions of the (2+ 1)-dimensional integrable Davey-Stewartson-type equation via a new method]]></article-title>
<source><![CDATA[Chaos, Solitons &amp; Fractals]]></source>
<year>2003</year>
<volume>18</volume>
<page-range>299</page-range></nlm-citation>
</ref>
<ref id="B25">
<label>25</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lü]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Jacobi elliptic function solutions for two variant Boussinesq equations]]></article-title>
<source><![CDATA[Chaos, Solitons &amp; Fractals]]></source>
<year>2005</year>
<volume>24</volume>
<page-range>1373</page-range></nlm-citation>
</ref>
<ref id="B26">
<label>26</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tala-Tebue]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Zayed]]></surname>
<given-names><![CDATA[E. M. E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[New Jacobi elliptic function solutions, solitons and other solutions for the (2+ 1)-dimensional nonlinear electrical transmission line equation]]></article-title>
<source><![CDATA[The European Physical Journal Plus]]></source>
<year>2018</year>
<volume>133</volume>
<page-range>314</page-range></nlm-citation>
</ref>
<ref id="B27">
<label>27</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pankaj]]></surname>
<given-names><![CDATA[R. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Singh]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Kumar]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[New extended Jacobi elliptic function expansion scheme for wave-wave interaction in ionic media]]></article-title>
<source><![CDATA[Nanosystems: Physics, Chemistry, Mathematics]]></source>
<year>2018</year>
<volume>9</volume>
<page-range>581</page-range></nlm-citation>
</ref>
<ref id="B28">
<label>28</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ebaid]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Aly]]></surname>
<given-names><![CDATA[E. H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Exact solutions for the transformed reduced Ostrovsky equation via the F-expansion method in terms of Weierstrass-elliptic and Jacobian-elliptic functions]]></article-title>
<source><![CDATA[Wave Motion]]></source>
<year>2012</year>
<volume>49</volume>
<page-range>296</page-range></nlm-citation>
</ref>
<ref id="B29">
<label>29</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pankaj]]></surname>
<given-names><![CDATA[R. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Kumar]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Lal]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A novel narration for two long waves interaction through the elaboration scheme]]></article-title>
<source><![CDATA[J. Inter. Maths.]]></source>
<year>2022</year>
<volume>25</volume>
<page-range>79</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
