Riemann–Hilbert approach for a higher-order Chen–Lee–Liu equation with high-order poles

Riemann-Hilbert approach and double-pole solutions for the third-order flow equation of DNLS-type equation with nonzero boundary conditions

“…In particular, for some implicit soliton solutions, it can be solved by revised Riemann-Hilbert approach [23,24]. It was also widely used in initial boundary value problem [25][26][27][28][29] and long-time asymptotics [30][31][32][33][34][35][36][37]. Due to the use of the inverse scattering transform method for solving equations often involves solving the GLM integral equation, which is not applicable for highdimensional spectral problems.…”

Lump solution and interaction solutions to the fourth-order extended (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

“…In recent years, many methods have been found to solve the exact solutions of soliton equations. For example, Hirota bilinear method [16][17][18], Generalized bilinear method [19,20], homogeneous balance method [21,22], Riemann-Hilbert method [23][24][25], Darboux transformation [26][27][28], Riccati expansion method [29,30] and so on. Hirota bilinear method is a common method to solve soliton equations, and Ma has solved many soliton equations with lump solutions and exact solutions by Hirota bilinear method [31].…”

“…Recently, Riemann-Hilbert method has been widely used to solve soliton solutions of equations. Explicit soliton solutions of a higher-order Chen-Lee-Liu equation [25], N-soliton solutions for the Maxwell-Bloch equations [32] are obtained by this method.…”