Lie symmetry analysis and exact solutions for the extended mKdV equation. (English) Zbl 1223.37079

Liu, Hanze; Li, Jibin

Acta Appl. Math. 109, No. 3, 1107-1119 (2010).

This paper concerns solutions of an extended mKdV equation of the form \[ u_t +a_1 u_{xxx} + a_2 u_x +a_3 u u_x + a_4 u^2 u_x = 0, \] where \(u = u(x,t)\) is an unknown function and the parameters \(a_i\) are real numbers with \(a_1 a_4 \neq 0\). Its exact solutions are obtained by using the method of Lie symmetry analysis as well as the method of dynamical systems, including the bifurcation and traveling wave solutions. The authors determine the conditions of the existence of such solutions and obtain exact analytic solutions by using the power series method.

Reviewer: Min Ho Lee (Cedar Falls)

MSC:

37K05	Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
17B80	Applications of Lie algebras and superalgebras to integrable systems
35A30	Geometric theory, characteristics, transformations in context of PDEs
35Q53	KdV equations (Korteweg-de Vries equations)

Keywords:

Lie symmetry analysis; bifurcations; traveling wave solutions; extended mKdV equations

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