In the present work, treating the arteries as a thin-walled and prestressed elastic tube with a stenosis and the blood as a Newtonian fluid with negligible viscosity, we have studied the amplitude modulation of nonlinear waves in such a composite system by use of the reductive perturbation method. The governing evolution equation was obtained as the variable coefficient nonlinear Schrödinger (N...

The nature of transverse instabilities of dark solitons for the (2+1)-dimensional defocusing nonlinear Schrödinger/Gross–Pitaevskĭi (NLS/GP) equation is considered. Special attention is given to the small (shallow) amplitude regime, which limits to the Kadomtsev–Petviashvili (KP) equation. We study analytically and numerically the eigenvalues of the linearized NLS/GP equation. The dispersion re...

Abstract We relate the scattering theory of focusing AKNS system with equally sized nonvanishing boundary conditions to that matrix Schrödinger equation. This (shifted) Miura transformation converts nonlinear (NLS) equation into a new nonlocal integrable apply triplet method solving Marchenko integral equations by separation variables derive multisoliton solutions this equation, thus proposing ...

We revisit the averaged equation, derived in Phys. Rev. Lett. 91, 240201 (2003)] from the nonlinear Schrödinger (NLS) equation with the nonlinearity management. We show that this averaged equation is valid only at the initial time interval, while a new Hamiltonian averaged NLS equation can be used at longer time intervals. Using the new averaged equation, we construct numerically matter-wave so...

We consider cnoidal traveling wave solutions to the focusing nonlinear Schrödinger equation (NLS) that have been shown to persist when the NLS is perturbed to the complex Ginzburg–Landau equation (CGL). We show that while these periodic traveling waves are spectrally stable solutions of NLS with respect to periodic perturbations, they are unstable with respect to bounded perturbations. Furtherm...

We consider two types of strongly localized modes in discrete nonlinear lattices. Taking the lattice nonlinear Schrodinger (NLS) equation as a particular but rather fundamental example, we show that (1) the discreteness effects may be understood in the "standard" discrete NLS model as arising from an effective periodic potential similar to the Peierls-Nabarro (PN) barrier potential for kinks in...

The widely used approach to study the beam propagation in Kerr media is based on the slowly varying envelope approximation (SVEA) which is also known as the paraxial approximation. Within this approximation, the beam evolution is described by the nonlinear Schrödinger (NLS) equation. In this paper, we extend the NLS equation by including higher order terms to study the effects of nonparaxiality...

We consider an integrable generalization of the nonlinear Schrödinger (NLS) equation that was recently derived by one of the authors using bi-Hamiltonian methods. This equation is related to the NLS equation in the same way that the Camassa Holm equation is related to the KdV equation. In this paper we: (a) Use the bi-Hamiltonian structure to write down the first few conservation laws. (b) Deri...

Persistence of stationary and traveling single-humped localized solutions in the spatial discretizations of the nonlinear Schrödinger (NLS) equation is addressed. The discrete NLS equation with the most general cubic polynomial function is considered. Constraints on the nonlinear function are found from the condition that the second-order difference equation for stationary solutions can be redu...

We show that a number of nonlocal nonlinear equations, including the Ablowitz–Musslimani and Yang variant Schrödinger (NLS) equation, modified Korteweg de Vries (mKdV) Hirota admit novel kinklike pulselike superposed periodic solutions. Furthermore, we mKdV equation also admits (hyperbolic) kink–antikink solution. In addition, while NLS complex parity-time reversal-invariant kink pulse solution...