Riemann–Hilbert approach of the complex Sharma–Tasso–Olver equation and its N-soliton solutions

Abstract

In this paper, we study the complex Sharma-Tasso-Olver equation via the Riemann-Hilbert approach. The associated Riemann-Hilbert problem for this integrable equation can be naturally constructed by considering the spectral problem of the Lax pair. Subsequently, in the case where the Riemann-Hilbert problem is irregular, the N-soliton solutions of the equation can be deduced. In addition, the three-dimensional graphic of the soliton solutions and wave propagation image are graphically depicted and further discussed.

Multi-soliton solutions of coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions

“…Furthermore, various methods have been proposed to deal with NLS-type equations, such as the inverse scattering transform, [22][23][24] Lie symmetry, [25][26][27] DT, [28] PINN method, [29,30] Hirota bilinear method, [31] and Riemann-Hilbert (RH) methods. [32][33][34][35] The RH method is associated with the RH problem, which helps simplify the original inverse scattering transform, and it has been proved as an efficient method for solving NLS-type equations. [36][37][38][39] However, under NZBC, the RH problem becomes more complex, [19][20][21] and thus only a few studies have used the RH method to explore the equations, which is the main focus of this paper.…”