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Traditional approaches to optical matter often involve complex illumination fields with costly and unstable setups, requiring strong gradient forces, high-intensity laser spots that could harm samples, and substrate support. For binding,…

We present a novel numerical framework for studying nonlinear dispersive equations in higher-dimensional settings, specifically designed for solutions featuring traveling waves along a preferred axis (or field-aligned traveling waves).…

The nonlinear Schr\"{o}dinger equation with variable coefficients has applications in numerous areas of physics,specifically in the context of nonlinear optics and Bose-Einstein condensate. Apart from the usual bright and dark-soliton…

In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…

The algebraic geometric approach to $N$-component systems of nonlinear integrable PDE's is used to obtain and analyze explicit solutions of the coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to anti-kink…

By constructing the general six-parameter bright two-soliton solution of the integrable coupled nonlinear Schrodinger equation (Manakov model) using the Hirota method, we find that the solitons exhibit certain novel inelastic collision…

Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase-transition point are analytically studied. A nonlinear Klein-Gordon equation is derived for the envelope of these wave packets. A variety of novel phenomena…

The existence of ``dispersion-managed solitons'', i.e., stable pulsating solitary-wave solutions to the nonlinear Schr\"{o}dinger equation with periodically modulated and sign-variable dispersion is now well known in nonlinear optics. Our…

Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations…

We analytically solved the higher-order nonlinear Schrodinger (HNLS) equation with non-Kerr nonlinearity under some parametric conditions and investigated explicitly bright and dark solitary wave solutions. Periodic wave solutions are also…

We reformulate the one-dimensional complex Ginzburg-Landau equation as a fourth order ordinary differential equation in order to find stationary spatially-periodic solutions. Using this formalism, we prove the existence and stability of…

We consider reaction-diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, coloured in space, and invariant under translations. In the deterministic setting,…

The existence of multidimensional lattice compactons in the discrete nonlinear Schr\"odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast…

The nonlinear Schrodinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas. However, due to the difficulty of solving this equation, in particular in high…

We construct and discuss a semi-rational, multi-parametric vector solution of coupled nonlinear Schr\"odinger equations (Manakov system). This family of solutions includes known vector Peregrine solutions, bright-dark-rogue solutions, and…

The paper deals with the studies of the nonlinear wave solutions supported by the modified FitzHugh-Nagumo (mFHN) system. It was proved in our previous work that the model, under certain conditions, possesses a set of soliton-like traveling…

We construct new exact solutions of the focusing Nonlinear Schr\"{o}dinger equation (NLSE). This is a soliton propagating on an unstable condensate. The Kuznetsov and Akhmediev solitons as well as the Peregrine instanton are particular…

Discrete solitons in the Ablowitz-Ladik (AL) and discrete nonlinear Schr\"odinger (DNLS) equations with damping and strong rapid drive are investigated. The averaged equations have the forms of the parametric AL and DNLS equations. A new…

In this paper, we study the novel nonlinear wave structures of a (2+1)-dimensional variable-coefficient Korteweg-de Vries (KdV) system by its analytic solutions. Its $N$-soliton solution are obtained via Hirota's bilinear method, and in…

We analyze the stationary and traveling wave solutions to a family of degenerate dispersive equations of KdV and NLS-type. In stark contrast to the standard soliton solutions for non-degenerate KdV and NLS equations, the degeneracy of the…