D'Alembert wave, the Hirota conditions and soliton molecule of a new generalized KdV equation

Abstract

A (2+1)-dimensional new generalized Korteweg-de Vries (ngKdV) equation is educed from a bilinear differential equation by combining the logarithmic transformation u=2(lnf)x. Depending on bilinear equation, we can compute the Hirota N-soliton condition and N-soliton solutions. The D'Alembert type waves of the (2+1)-dimensional ngKdV equation are shown via introducing traveling-wave variables. By dealing with the matching bilinear form, the multiple solitary solution that should fulfill the velocity resonance condition is found in the egKdV equation. Some of the figures of two-soliton molecules and three-soliton molecules are obtained by determining the appropriate arguments.