Solitary wave solutions to the generalized coupled mKdV equation with multi-component

Abstract

Using the Darboux matrix method, the multi-solitary wave solutions of the generalized coupled mKdV equation with multi-component are obtained. The obtained solution formulas provide us with a comprehensive approach to construct exact solutions for the generalized coupled mKdV equation by some basic solutions of the Boiti and Tu spectral problem.

Exact traveling soliton solutions for the scalar Qiao equation

“…Thus S b maps a solution of equation ( 1) to another solution of equation ( 1) because equation ( 8) implies equation (7).…”

“…Many powerful methods have been presented to investigate exact solutions of nonlinear equations, such as the homogeneous balance method [1], the tanh method [2,3], the inverse scattering transform, the exp-function expansion method [4,5], the Darboux matrix method [6][7][8][9][10], the Jacobi elliptic function expansion [11,12], the subequation method [13], the tanh and sine-cosine function methods [14,15], the auxiliary equation method [16][17][18] and the nonlocal symmetries method [19][20][21]. Thus, Xu [22] exposed various algebraic techniques of solving partial differential equations for exact solutions developed by several authors in recent years.…”

N-soliton solutions of an integrable equation studied by Qiao

“…(1) using the Darboux matrix method. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] This paper is organized as follows. In Section 2, a chain of new transformations are introduced to relate Eq.…”