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Under investigation in this paper is a coupled nonlinear Schrödinger (NLS) equation, which describes nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order. Based on the Lax pair of the coupled NLS equation, we construct the determinant representation of the N -fold Darboux transformation(DT). Furthermore, by using the obtained N -fold DT, we obtain its higher-order soliton, breather and rogue wave solutions. Finally, the dynamic characteristics of these solutions are discussed. [ABSTRACT FROM AUTHOR]

In this work, we study the dynamic properties of the transformed nonlinear waves of the six-order nonlinear Schrödinger equation. The breather wave of the equation is obtained based on the Darboux transformation. In order to study the state transition, we give the transition conditions of the breather wave. Based on this transition condition, the breather wave is transformed into various types of nonlinear waves, including W-shaped solitons, M-shaped solitons, multi-peak solitons, oscillation solitons, etc. Furthermore, the oscillation properties of these transformed nonlinear waves are analyzed. Finally, these transformed nonlinear waves are graphically presented. [ABSTRACT FROM AUTHOR]

Abstract We consider the Heisenberg ferromagnetic spin chain equation, which is governed by the (2+1)-dimensional nonlinear Schrödinger-type equation. Based on the Ablowitz–Kaup–Newell–Segur frame, we study the integrability of the equation by deriving its Lax pair and infinite conservation laws. By introducing a potential transformation, we obtain its Hirota bilinear form and soliton solutions. Based on the resulting lax pair, we construct Darboux transformation and multi-soliton solutions of the equation. Furthermore, we also find the other type of soliton solutions for the equation by considering its Bäcklund transformation. Finally, we discuss the linear stability analysis by considering its stability condition for the stationary solution of the equation, which can be used to analyze modulation instability. The technique presented in this work is analytical, which can be used to enrich the dynamical of the Heisenberg ferromagnetic spin chain equation. [ABSTRACT FROM AUTHOR]

An integrable three-component coupled nonlinear Schrödinger (NLS) equation is considered in this work. We present the scattering and inverse scattering problems of the three-component coupled NLS equation by using the Riemann–Hilbert formulation. Furthermore, according to the Riemann–Hilbert method, the multi-soliton solutions of this equation are derived. We also analyze the collision dynamic behaviors of these solitons. Moreover, a new phenomenon for two-soliton collision is displayed, which is unique and not common in integrable systems. It is hoped that our results can help enrich the nonlinear dynamics of the NLS-type equations. [ABSTRACT FROM AUTHOR]