1999•Acta Physica SinicaOpen access

EXACT SOLITON SOLUTIONS OF THE VARIABLE COEFFICIENT KdV-MKdV EQUATION WITH THREE ARBITRARY FUNTIONS

YAN ZHEN-YA, Hongqing Zhang, 大连理工大学数学科学研究所，大连 116024

Abstract

In this paper,first,by using a new transformation,the variable coefficient KdV-MKdV equation is reduced to a third-order nonlinear ordinary differential equation (NODE),and then several exact soliton-solutions for the variable coefficient KdV-MKdV equatioin are obtained through considering this NODE.The method can be also used to solve other nonlinear equations,such as the variable coefficient KP equation,sine-Gordon equation and so on.

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Key concepts: Korteweg–de Vries equation, Variable coefficient, sine-Gordon equation, Variable (mathematics), Soliton, Nonlinear system, Ordinary differential equation, Transformation (genetics)