Auto-Bäcklund transformations and superposition formulas for solutions of Drinfeld–Sokolov systems

On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation

“…It should be pointed out that the two-component mYOLS Equation (10) is different from the long-wave-short-wave resonance Equation (1), and the two-component mYOLS Equation (10) is equivalent to the long-wave-short-wave model (2) under some transformation [21]. Then, with the help of Riccati equations for the Lax pair associated with the vmYOLS Equation (8) [22][23][24], Bäcklund transformation [25,26], Darboux transformation [27][28][29][30][31][32][33][34][35][36][37][38][39], and others [40][41][42][43][44][45][46][47][48][49][50][51]. Some interesting explicit solutions have been found, the most important among which are pure-soliton solutions, quasi-periodic solutions, and rogue waves solutions.…”

Soliton, breather, lump and their interaction solutions of the ($2+1$)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation

“…A set of systematic methods have been used in the literature to obtain reliable treatments of nonlinear evolution equations. So far, researchers have established several methods to find the exact solutions, including the inverse scattering transform [1], the Bäcklund transformation [2][3][4][5], the Darboux transformation [6][7][8][9][10][11][12][13][14], the Riemann-Hilbert approach [15][16][17] and Hirota's bilinear method [18][19][20][21][22][23][24][25][26][27][28], Jacobian elliptic function method and modified tanh-function method [29][30][31][32][33]. Each of these approaches has its features, Hirota's bilinear method is widely popular due to its simplicity and directness.…”