The Landau-Lifshitz-Gilbert (LLG) equation is a fascinating nonlinear evolution both from mathematical and physical points of view. It related to the dynamics several important systems such as ferromagnets, vortex filaments, moving space curves, etc. has intimate connections with many well known integrable soliton equations, including Schr\"odinger sine-Gordon equations. can admit very dynamical structures spin waves, elliptic function solitons, dromions, vortices, spatio-temporal patterns,...

We study the existence of chimera states in pulse-coupled networks bursting Hindmarsh-Rose neurons with nonlocal, global, and local (nearest neighbor) couplings. Through a linear stability analysis, we discuss behavior function incoherent (i.e., disorder), coherent, chimera, multichimera states. Surprisingly, find that occur even using nearest neighbor interaction network identical alone. This is contrast populations nonlocally or globally coupled oscillators. A chemical synaptic coupling...

By constructing the general six-parameter bright two-soliton solution of integrable coupled nonlinear Schr\"odinger equation (Manakov model) using Hirota method, we find that solitons exhibit certain novel inelastic collision properties, which have not been observed in any other $(1+1)$-dimensional soliton system so far. In particular, identify exciting possibility switching between modes by changing phase. However, standard elastic property is regained with specific choices parameters.

We present the exact bright one-soliton and two-soliton solutions of integrable three coupled nonlinear Schroedinger equations (3-CNLS) by using Hirota method, then obtain them for general $N$-coupled (N-CNLS). It is pointed out that underlying solitons undergo inelastic (shape changing) collisions due to intensity redistribution among modes. also analyse various possibilities conditions such occur. Further, we report significant fact partial coherent (PCS) discussed in literature are...

A set of two coupled nonlinear Schrodinger equations (CNLS) describes the mode propagation in an optical fibre. The Painleve singularity structure analysis singles out integrable parametric choices, including Manakov model. Using results analysis, we succeed Hirota bilinearizing CNLS both anomalous as well normal dispersion regions for cases. Solving bilinear equations, bright and dark N-soliton solutions are explicitly obtained.

The integrability aspects of a classical one-dimensional continuum isotropic biquadratic Heisenberg spin chain in its limit up to order [O(a4)] the lattice parameter ‘‘a’’ are studied. Through differential geometric approach, dynamical equation for is expressed form higher-order generalized nonlinear Schrödinger (GNLSE). An integrable that deformation lower-order chain, identified by carrying out Painlevé singularity structure analysis on GNLSE (also through gauge analysis) and properties...

Mixed type (bright-dark) soliton solutions of the integrable N-coupled nonlinear Schr{\"o}dinger (CNLS) equations with mixed signs focusing and defocusing nonlinearity coefficients are obtained by using Hirota's bilinearization method. Generally, for N-CNLS bright dark solitons can be split up in $(N-1)$ ways. By analysing collision dynamics these coupled systematically we point out that $N>2$, if appear at least two components, non-trivial effects like onset intensity redistribution,...

A different kind of shape changing (intensity redistribution) collision with potential application to signal amplification is identified in the integrable -coupled nonlinear Schrödinger (CNLS) equations mixed signs focusing- and defocusing-type nonlinearity coefficients. The corresponding soliton solutions for N=2 case are obtained by using Hirota's bilinearization method. distinguishing feature sign CNLS that can both be singular regular. Although general solution admits singularities we...

By developing the concepts of strength incoherence and discontinuity measure, we show that a distinct quantitative characterization chimera multichimera states which occur in networks coupled nonlinear dynamical systems admitting nonlocal interactions finite radius can be made. These measures also clearly distinguish between or (both stable breathing types) coherent incoherent as well cluster states. The provide straightforward precise various chaotic irrespective complexity underlying attractors.

We present explicit forms of general breather (GB), Akhmediev (AB), Ma soliton (MS), and rogue wave (RW) solutions the two-component nonlinear Schr\"odinger (NLS) equation, namely Manakov equation. derive these through two different routes. In forward route, we first construct a suitable periodic envelope solution to this model from which GB, AB, MS, RW solutions. then consider as starting point GB in reverse direction. The second approach has not been illustrated so far for component NLS...

It is known that Manakov equation which describes wave propagation in two mode optical fibers, photorefractive materials, etc. can admit solitons allow energy redistribution between the modes on collision also leads to logical computing. In this paper, we point out system more general type of nondegenerate fundamental corresponding different numbers, undergo collisions without any redistribution. The previously class allows among turns be a special case solitary waves with identical numbers...

The novel dynamical features underlying soliton interactions in coupled nonlinear Schr{\"o}dinger equations, which model multimode wave propagation under varied physical situations optics, are studied. In this paper, by explicitly constructing multisoliton solutions (upto four-soliton solutions) for two and arbitrary $N$-coupled equations using the Hirota bilinearization method, we bring out clearly various fascinating shape changing (intensity redistribution) collisions of solitons,...

We investigate the phenomenon of chaos synchronization and efficient signal transmission in a physically interesting model, namely, Van der Pol--Duffing oscillator. A criterion for based on asymptotic stability is discussed. By considering cascaded system, we possibility secure communication analog signals.

In this paper, we present the hyperchaos dynamics of a modified canonical Chua's electrical circuit. This circuit, which is capable realizing behavior every member family, consists just five linear elements (resistors, inductors and capacitors), negative conductor piecewise resistor. The route followed transition from regular to chaos then through border-collision bifurcation, as system parameter varied. dynamics, characterized by two positive Lyapunov exponents, described set four coupled...

We propose an integrable system of coupled nonlinear Schrödinger equations with cubic-quintic terms describing the effects quintic nonlinearity on ultrashort optical soliton pulse propagation in non-Kerr media. Lax pairs, conserved quantities and exact solutions for proposed model are given. The explicit form two solitons used to study interaction showing many intriguing features including inelastic (shape changing or intensity redistribution) scattering. Another fifth-degree is derived,...

We show by computer simulation that chaos can occur in a sinusoidally driven second-order circuit made of three linear elements and Chua's diode. Unlike many other nonautonomous chaotic circuits whose nonlinear element is capacitor, the diode resistor, therefore simpler from circuit-theoretic point view.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>