Vector solitons and rogue waves of the matrix Lakshmanan–Porsezian–Daniel equation

Nonlinear Dynamics - With the Darboux-dressing transformation, we study the vector solitons and rogue waves of the matrix Lakshmanan–Porsezian–Daniel equation. Firstly, we show the...     

N-fold generalized Darboux transformation and breather–rogue waves on the constant/periodic background for a generalized mixed nonlinear Schrödinger equation

Nonlinear Dynamics - In this paper, a generalized mixed nonlinear Schrödinger equation, which arises in several physical applications including fluid mechanics (for the weakly nonlinear...     

Solitons and rogue waves of the quartic nonlinear Schrödinger equation by Riemann–Hilbert approach

Nonlinear Dynamics - We systematically develop a Riemann–Hilbert approach for the quartic nonlinear Schrödinger equation on the line with both zero boundary condition and nonzero...     

Breathers,solitons and rogue waves of the quintic nonlinear Schrödinger equation on various backgrounds

Nonlinear Dynamics - We investigate the generation of breathers, solitons, and rogue waves of the quintic nonlinear Schrödinger equation (QNLSE) on uniform and elliptical backgrounds. The...     

Group classification and exact solutions of a generalized Emden–Fowler equation

The aim of this work is to perform a complete symmetry classification of a generalized Emden-Fowler equation. The various forms of this equation are extensively studied in the literature and they have applications in astrophysical and physiological phenomena. The classical approach of group classification and the procedure based upon the Lie algebras of low dimension are employed for classification. Exact solutions of the invariant equations are derived.     

Characteristics of the solitary waves and lump waves with interaction phenomena in a (2 + 1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation

In this paper, we consider a (\(2+1\))-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada (gCDGKS) equation, which is a higher-order generalization of the celebrated Kadomtsev–Petviashvili (KP) equation. By considering the Hirota bilinear form of the CDGKS equation, we study a type of exact interaction waves by the way of vector notations. The interaction solutions, which possess extensive applications in the nonlinear system, are composed by lump wave parts and soliton wave parts, respectively. Under certain conditions, this kind of solutions can be transformed into the pure lump waves or the stripe solitons. Moreover, we provide the graphical analysis of such solutions in order to better understand their dynamical behavior.     

General high-order rogue waves to nonlinear Schrödinger–Boussinesq equation with the dynamical analysis

Nonlinear Dynamics - General high-order rogue waves of the nonlinear Schrödinger–Boussinesq equation are obtained by the KP-hierarchy reduction theory, and the N-order rogue waves are...     

Boundary control of the generalized Korteweg–de Vries–Burgers equation

This paper considers the boundary control problem of the generalized Korteweg–de Vries–Burgers (GKdVB) equation on the interval [0, 1]. We derive a control law of the form and α is a positive integer, and prove that it guarantees L ²-global exponential stability, H ¹-global asymptotic stability, and H ¹-semiglobal exponential stability. Numerical results supporting the analytical ones for both the controlled and uncontrolled equations are presented using a finite element method.     

Soliton,breather and rogue wave solutions of the coupled Gerdjikov–Ivanov equation via Darboux transformation

Nonlinear Dynamics - The coupled Gerdjikov–Ivanov (cGI) equation, associated with a $$3times 3$$ matrix Lax pair, is an important integrable system that can be reduced to the third kind of...     

Solitons and periodic waves for the (2 + 1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics

Nonlinear Dynamics - Fluid mechanics has the applications in a wide range of disciplines, such as oceanography, astrophysics, meteorology, and biomedical engineering. Under investigation in this...