Two-dimensional structures in the quintic Ginzburg–Landau equation
نویسندگان
چکیده
منابع مشابه
The Quintic Nonlinear Schrödinger Equation on Three-dimensional Zoll Manifolds
Let (M, g) be a three-dimensional smooth compact Riemannian manifold such that all geodesics are simple and closed with a common minimal period, such as the 3-sphere S with canonical metric. In this work the global well-posedness problem for the quintic nonlinear Schrödinger equation i∂tu+∆u = ±|u|u, u|t=0 = u0 is solved for small initial data u0 in the energy space H(M), which is the scaling-c...
متن کاملNUMERICAL SOLUTION OF ONE-DIMENSIONAL HEAT AND WAVE EQUATION BY NON-POLYNOMIAL QUINTIC SPLINE
This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed metho...
متن کاملDifferential Transform Method to two-dimensional non-linear wave equation
In this paper, an analytic solution is presented using differential transform method (DTM) for a class of wave equation. The emphasis is on the nonlinear two-dimensional wave equation. The procedures introduced in this paper are in recursive forms which can be used to obtain the closed form of the solutions, if they are required. The method is tested on various examples, and the results reveal ...
متن کاملStable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation.
We demonstrate the existence of stable toroidal dissipative solitons with the inner phase field in the form of rotating spirals, corresponding to vorticity S=0, 1, and 2, in the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity. The stable solitons easily self-trap from pulses with embedded vorticity. The stability is corroborated by accurate computation of growth rates for p...
متن کاملExact Solutions of the One-Dimensional Quintic Complex Ginzburg-Landau Equation
Exact solitary wave solutions of the one-dimensional quintic complex Ginzburg-Landau equation are obtained using a method derived from the Painlevé test for integrability. These solutions are expressed in terms of hyperbolic functions, and include the pulses and fronts found by van Saarloos and Hohenberg. We also find previously unknown sources and sinks. The emphasis is put on the systematic c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinear Dynamics
سال: 2015
ISSN: 0924-090X,1573-269X
DOI: 10.1007/s11071-015-2077-2