Darboux transformation of a two‐component generalized Sasa–Satsuma equation and explicit solutions

Abstract

Under investigation in this paper is a two‐component generalized Sasa–Satsuma equation associated with a 4 × 4 matrix spectral problem. We construct Darboux transformation for the two‐component generalized Sasa–Satsuma equation on basis of the gauge transformation between the Lax pairs. The corresponding N‐fold Darboux transformation is derived in terms of both iterative representation and compact determinant form. As applications of the Darboux transformation together with the limit technique, some interesting solutions including traveling soliton solutions, breather soliton solutions, and rogue wave solutions are explicitly obtained and graphically illustrated.

Time-fractional Davey–Stewartson equation: Lie point symmetries, similarity reductions, conservation laws and traveling wave solutions

“…where ò is a parameter. Soving equation (22) results in : , , , , , , , , , , , : , , , , , , , , , , , : , , , , , , , , cos sin , sin cos , .…”

“…In the last few decades, researchers have paid much attention to the study of NPDEs, including their dynamic properties and solutions. A number of methods were put forward to acquire the solutions of NPDEs, for example, the homogeneous balance method [10][11][12][13], inverse scattering transform [14][15][16][17][18], Darboux transformation [19][20][21][22][23][24], Hirota's bilinear method [25][26][27][28][29][30][31][32][33], Riemann-Hilbert approach [34][35][36][37][38][39][40][41][42][43], nonlocal symmetry method and so on [44][45][46][47][48][49]. However, for most NPDEs, the solutions are difficult to obtain due to their complex expressions.…”