Bright solitons and multiple soliton solutions for coupled modified KdV equations with time-dependent coefficients

Abstract

Two coupled modified KdV (mKdV) equations are investigated. The first coupled mKdV equation, with time-dependent coefficients, is derived from a two-layer fluid system. The second coupled mKdV equation, with constant coefficients, is derived from the first one. We make use of the soliton ansatz to determine bright solitons for the first model. The simplified form of Hirota's bilinear method, developed by Hereman, is used to examine the complete integrability and to derive multiple soliton solutions for the second model. Bright solitons, multiple soliton solutions and multiple singular soliton solutions are obtained for these coupled equations.

Optical soliton solutions for the variable coefficient modified Kawahara equation

“…We start the analysis by assuming a solitary wave ansatz of the form [32,33] u(x; t) = sech p ( (x vt));…”

“…Thus, …nally, the dark 1-soliton solution for the variable coe¢ cient modi…ed Kawahara equation (VCMKE) when we substitude (31), (33), (40) and (42) in (24) as…”