Results 71 to 80 of about 1,098 (97)

Multi-scale Analysis of Nonlinear Equations [PDF]

arXiv, 2002
We use a multi-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain.
arxiv  

Knotted solitons [PDF]

Proceedings of the ICM, Beijing 2002, vol. 1, 235--244, 2002
The dynamical model on 3+1 dimensional spacetime admitting soliton solutions is discussed. The proposal soliton is localized in the vicinity of a closed contour, which could be linked and/or knotted. The topological charge is Hopf invariant. Some applications in realistic physical systems are indicated.
arxiv  

A family of conformally flat Hamiltonian-minimal Lagrangian tori in $\mathbb{CP}^3$ [PDF]

arXiv, 2008
In this paper by reduction we construct a family of conformally flat Hamiltonian-minimal Lagrangian tori in $\mathbb{CP}^3$ as the image of the composition of the Hopf map $\mathcal{H}: \mathbb{S}^7\to \mathbb{CP}^3$ and a map $\psi:\mathbb{R}^3 \to \mathbb{S}^7$ with certain conditions.
arxiv  

Slow passage through parametric resonance for a weakly nonlinear dispersive wave [PDF]

arXiv, 2008
A solution of the nonlinear Klein-Gordon equation perturbed by a parametric driver is studied. The frequency of the parametric perturbation varies slowly and passes through a resonant value. It yields a change in a solution. We obtain a connection formula for the asymptotic solution before and after the resonance.
arxiv  

Two soliton solutions to the three dimensional gravitational Hartree equation [PDF]

arXiv, 2008
We construct non dispersive two soliton solutions to the three dimensional gravitational Hartree equation whose trajectories asymptotically reproduce the nontrapped dynamics of the gravitational two body problem.
arxiv  

Asymptotics of the solitary waves for the generalised Kadomtsev-Petviashvili equations [PDF]

Discrete and Continuous Dynamical Systems: Series A 21, 3 (2008) 835-882, 2009
We investigate the asymptotic behaviour of the localised solitary waves for the generalised Kadomtsev-Petviashvili equations. In particular, we compute their first order asymptotics in any dimension $N \geq 2$.
arxiv  

Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation arising in the topic of neuroscience

Partial Differential Equations in Applied Mathematics
Time-space fractional nonlinear problems (T-SFNLPs) play a crucial role in the study of nonlinear wave propagation. Time-space nonlinearity is prevalent across various fields of applied science, nonlinear dynamics, mathematical physics, and engineering ...
Md. Nur Alam, Md. Azizur Rahman
doaj  

Abscence of embedded spectrum for nonlinear Schrödinger equations linearized around one dimensional ground states [PDF]

arXiv
We consider the nonlinear Schr\"odinger equation in dimension one for a generic nonlinearity. We show that ground states do not have embedded eigenvalues in the essential spectrum of their linearized operators.
arxiv  

Modulational Instability of Small Amplitude Periodic Traveling Waves in the Novikov Equation [PDF]

arXiv
We study the spectral stability of smooth, small-amplitude periodic traveling wave solutions of the Novikov equation, which is a Camassa-Holm type equation with cubic nonlinearities. Specifically, we investigate the $L^2(\mathbb{R})$-spectrum of the associated linearized operator, which in this case is an integro-differential operator with periodic ...
arxiv  

Investigation of new solitary stochastic structures to the Heisenberg ferromagnetic spin chain model via a Stratonovich sense

Partial Differential Equations in Applied Mathematics
This study examines how Stratonovich integrals (SIs) affect the solutions of the Heisenberg ferromagnetic spin chain (HFSC) equation using the modified (G'/G)-expansion (MG'/GE) scheme.
Md. Nur Alam
doaj