N -soliton solutions for the nonlocal two-wave interaction system via the Riemann–Hilbert method

Abstract

In this paper, a nonlocal two-wave interaction system from the Manakov hierarchy is investigated via the Riemann-Hilbert approach. Based on the spectral analysis of the Lax pair, a Riemann-Hilbert problem for the nonlocal two-wave interaction system is constructed. By discussing the solutions of this Riemann-Hilbert problem in both the regular and nonregular cases, we explicitly present the N-soliton solution formula of the nonlocal two-wave interaction system. Moreover, the dynamical behaviour of the single-soliton solution is shown graphically.

Analytical manner for abundant stochastic wave solutions of extended KdV equation with conformable differential operators

“…From the nature of trigonometric and exponential functions, we realize that there are an open bounded set D ∈ R × R + , 𝜌 > 0 and 𝜋 < ∞, such that the solutions (20), ( 24), (27), and (30) and their conformable derivatives in (13) are uniformly bounded on D ×  𝜋 (𝜌). Further, they continue on D and analytic on  𝜋 (𝜌).…”

“…[4][5][6][7][8] The checking of accurate and rough solutions of nonlinear development conditions plays a critical activity in the investigation of nonlinear physical questions. Numerous accommodating strategies, for example, bilinear change strategy, 9 the adjusted Clarkson and Kruskal (CK) direct strategy, 10 the multiscale extension strategy, 11 the binary Bell polyno-mials strategy, 12 the Riemann-Hilbert strategy, 13 the surmised balance strategy, 14 and the overall improved Kudryashov strategy 15 have been introduced in the ongoing writing.…”

The Modified Coupled Hirota Equation: Riemann-Hilbert Approach and N-Soliton Solutions

“…Moreover, we mention that a nonlocal two-wave interaction system associated with an easier 3×3 matrix spectral problem is investigated with the aid of the Riemann-Hilbert approach by [25]. Let us study (2) for the localized solutions; we simply suppose that the potentials u and v decay to zero sufficiently fast as 푥 㨀→ ±∞, and 휖 is taken to be positive without loss of generality.…”

Exact solutions of stochastic fractional Korteweg de–Vries equation with conformable derivatives

“…[2,11] The investigation of exact and approximate solutions of nonlinear evolution equations plays an important role in the study of nonlinear physical phenomena. Many helpful methods such as bilinear transformation method, [35] the modified Clarkson and Kruskal (CK) direct method, [39] the multi-scale expansion method, [33] the binary Bell polynomials method, [48] the Riemann-Hilbert method, [41] and the approximate symmetry method [28] have been presented in the recent literature. He and Wu [19] introduced a concise and straightforward method, called the Exp-function method, to obtain generalized soliton, periodic, and compacton-like solutions for many nonlinear PDEs.…”