Darboux transformation and multi-soliton solutions of Boussinesq–Burgers equation

Painlevé property, Lax pair and Darboux transformation of the variable-coefficient modified Kortweg-de Vries model in fluid-filled elastic tubes

“…As we know, a gauge transformation of a spectral problem is called a Darboux transformation of such spectral problem if it transforms the spectral problem into another spectral problem of the same type [44]. Now we assume that…”

Vadermonde-Type Odd-Soliton Solutions for the Whitham–Broer–Kaup Model in the Shallow Water Small-Amplitude Regime

“…Darboux transformations (DTs) based on the Lax pair are a method to get the soliton solutions of some NLEEs from the seeds . Especially, the N -fold DT, which can be interpreted as the superposition of a single DT, has been applied to certain NLEEs for deriving the multi-soliton solutions [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Advantage of the N -fold DT is that the problem solving of a NLEE is finally reduced to solve a linear system, which enables us to generate the multi-soliton solutions [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] with symbolic computation [1][2][3][4][5][6][7][8][9][10][11][12].…”

Exact Solutions to the Boussinesq-Burgers Equations

“…In the present paper, we will investigate the well-known Boussinesq-Burgers equations in the form by many authors with different methods (see [1]- [6] and references therein).…”