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General symmetry approach to Solve Variable—Coefficient Nonlinear Equations

Communications in Theoretical Physics 2001年第6期35卷 641-646页

作者： RUANHang－Yu CHENYi－Xin 等 InstituteofModernPhysics NingboUniversityNingbo315211China ZhejiangInstituteofModernPhysics Zhejian

After considering the variable coefficient of a nonlinear equation as a new dependent variable, some special types of variable-coefficient equation can be solved from the corresponding constant-coefficient equations by using the general classical Lie approach. Taking the nonlinear Schr?dinger equation as a concrete example, the method is recommended in detail.

关键词： symmetry approach variable coefficient equation

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Lie symmetry analysis and invariant solutions for(2+1) dimensional Bogoyavlensky-Konopelchenko equation with variable-coefficient in wave propagation

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Journal of Ocean Engineering and Science 2022年第3期7卷 248-254页

作者： Mohamed R.Ali Wen-Xiu Ma R.Sadat Department of Basic Science Faculty of Engineering at BenhaBenha UniversityBenhaEgypt Department of Mathematics Zhejiang Normal UniversityJinhua 321004ZhejiangChina Department of Mathematics King Abdulaziz UniversityJeddah 21589Saudi Arabia Department of Mathematics and Statistics University of South FloridaTampaFL 33620-5700USA School of Mathematics South China University of TechnologyGuangzhou 510640China Department of Mathematics Zagazig Faculty of EngineeringZagazig UniversityZagazigEgypt

This work aims to present nonlinear models that arise in ocean *** are many models of ocean waves that are present in *** shallow water,the linearization of the equations requires critical conditions on wave capacity than it make in deep water,and the strong nonlinear belongings are *** use Lie symmetry analysis to obtain different types of soliton solutions like one,two,and three-soliton solutions in a(2+1)dimensional variable-coefficient Bogoyavlensky Konopelchenko(VCBK)equation that describes the interaction of a Riemann wave reproducing along the y-axis and a long wave reproducing along the x-axis in engineering and *** use the Lie symmetry analysis then the integrating factor method to obtain new solutions of the VCBK *** demonstrate the physical meaning of the solutions obtained by the presented techniques,the graphical performance has been demonstrated with some *** presented equation has fewer dimensions and is reduced to ordinary differential equations using the Lie symmetry technique.

关键词： symmetry approach Solitons Partial differential equations The variable coefficients(2+1)-dimensional Bogoyavlensky Konopelchenko equation Nonlinear evolution equations

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