On the Riemann–Hilbert problem for the mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation

Dynamic behaviors of soliton solutions for a three-coupled Lakshmanan–Porsezian–Daniel model

“…The main idea of this method is to establish a corresponding matrix RH problem on the Lax pair of integrable equations. Furthermore, the RH approach is also an effective way to examine the initial boundary value problems [28,29,30,31,32] and the long-time asymptotic behavior [33,34] of the integrable nonlinear evolution equations.…”

Applications for mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation in water wave flumes and optical fibers

“…The NLSE, that have linear, nonlinear dissipative and dispersive effects, provides the evolution of slowly altering packets of monochromatic waves in various systems [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. The MCLLNLS-equation is given as follows [40,41],…”

“…Many researchers worked on governing model, for instance Fang et al studied the N-soliton solutions and Riemann-Hilbert method for MCLLNLS-equation [40], Hu et al worked on Eq. ( 1) by using Riemann-Hilbert problem [41], Hu et al worked on dynamic of the smooth positons of the higher-order Chen-Lee-Liu model [42], Biswas investigated Chirp-free solitons for Chen-Lee-Liu equation by semi-inverse variational principle and traveling wave hypothesis [43], Baskonus et al worked for pulse propagation to the perturbed Chen-Lee-Liu model in fibers [44], the purpose of this manuscript is to evaluate Multiwaves solutions, Homoclinic breather, kink cross-rational and periodic cross-rational results, M −shaped rational and their interactions with one and two kink waves by applying the symbolic computation with ansatz functions approach and logarithmic transformation for Eq. ( 1).…”

Riemann–Hilbert Problem Associated with the Fourth-Order Dispersive Nonlinear Schrödinger Equation in Optics and Magnetic Mechanics

“…In the past 24 years, IBVPs of some classical integrable equations have be discussed via the Fokas method. For example, the modified Korteweg-de Vries (MKdV) equation [7], the nonlinear Schrödinger (NLS) equation [8], the Kaup-Newell equation [9], the stationary axisymmetric Einstein equations [10], the Ablowitz-Ladik system [11], the Kundu-Eckhaus equation [12], the Hirota equation [13,14] and other equations [15][16][17][18]. In 2012, Lenells extended the Fokas method to the integrable equation with higher-order matrix spectrum, he proposed a more general unified transformation approach to solve IBVPs of integrable models [19] and he used the unified transformation approach to analyze IBVPs of Degasperis-Procesi equation [20].…”