The field of nonlinear dispersive waves has developed enormously since the work of Stokes,
Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s …

Optical collapse is a fascinating research topic. The propagation of intense laser beams in a
transparent medium is usually modeled by the two-dimensional nonlinear Schrödinger …

A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-
wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of …

Three new iteration methods, namely the squared‐operator method, the modified squared‐
operator method, and the power‐conserving squared‐operator method, for solitary waves in …

We report the existence and stability of lattice solitons in parity-time (PT)-symmetric mixed
linear-nonlinear optical lattices in Kerr media. We focus on studying the characteristic effects …

In quantum theory, any Hamiltonian describing a physical system is mathematically
represented by a self-adjoint linear operator to ensure the reality of the associated …

In this paper, the Newton-conjugate-gradient methods are developed for solitary wave
computations. These methods are based on Newton iterations, coupled with conjugate …

We show that defocusing Kerr media with parity-time-symmetric potentials can support one-
and two-dimensional bright spatial solitons. These solitons are found to be stable over the …

The classical equations of water waves are reformulated as a system of two equations, one
of which is an explicit non-local equation, for the wave height and for the velocity potential …

Two accelerated imaginary‐time evolution methods are proposed for the computation of
solitary waves in arbitrary spatial dimensions. For the first method (with traditional power …