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1.
We consider global solutions of the nonlinear Schrödinger equation
相似文献
2.
A new class of exact solutions with a singularity at finite time (collapse) is obtained for the nonlinear Schrödinger equation. 相似文献
3.
《Physica D: Nonlinear Phenomena》1988,32(1):83-106
Using the multiscale approach of Zakharov and Kuznetsov it is shown that the nonlinear Schrödinger periodic scattering data is related to the Korteweg-de Vries periodic scattering data via an average over the Korteweg-de Vries carrier oscillation. This allows a complete elucidation of the physical meaning of the nonlinear Schrödinger scattering data, conservation laws, theta function solutions and reality constraint. 相似文献
4.
《Physica D: Nonlinear Phenomena》1988,31(1):78-102
A method of dynamic rescaling of variables is used to investigate numerically the nature of the focusing singularities of the cubic and quintic Schrödinger equations in two and three dimensions and describe their universal properties. The same method is applied to simulate the multi-focusing phenomena produced by simple models of saturating nonlinearities. 相似文献
5.
《Physica D: Nonlinear Phenomena》1988,32(2):210-226
For the cubic Schrödinger equation in two dimensions we construct a family of singular solutions by perturbing slightly the dimension d = 2 tod > 2. 相似文献
6.
Yu. N. Ovchinnikov 《Journal of Experimental and Theoretical Physics》2003,96(5):975-981
It is shown that one of the conditions for a weakly collapsing solution with zero energy produces an infinite number of functionals I N identically vanishing on the regular solutions to the corresponding differential equation. On the parameter plane {A, C1}, there are at least two singular lines. Along one of these lines (A/C1=1/6), are located weakly collapsing solutions with zero energy. It is assumed that, along the second line (A/C1=αc), another family of weakly collapsing solutions with zero energy is located. In the domain of large values of the parameters C1, α=A/C1, there exists a domain of an intermediate asymptotic form, where the amplitude of oscillations of the function U grows in a large domain relative to the ξ coordinate. 相似文献
7.
S. Murugesh Radha Balakrishnan 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(2):193-196
We apply our recent formalism establishing new connections between the geometry of moving space curves and soliton equations,
to the nonlinear Schr?dinger equation (NLS). We show that any given solution of the NLS gets associated with three distinct
space curve evolutions. The tangent vector of the first of these curves, the binormal vector of the second and the normal
vector of the third, are shown to satisfy the integrable Landau-Lifshitz (LL) equation = ×, ( = 1). These connections enable us to find the three surfaces swept out by the moving curves associated with the NLS. As an
example, surfaces corresponding to a stationary envelope soliton solution of the NLS are obtained.
Received 5 December 2001 Published online 2 October 2002
RID="a"
ID="a"e-mail: radha@imsc.ernet.in 相似文献
8.
9.
Nauman Raza Sultan Sial Shahid S. Siddiqi Turab Lookman 《Journal of computational physics》2009,228(7):2572-2577
In this the window of the Sobolev gradient technique to the problem of minimizing a Schrödinger functional associated with a nonlinear Schrödinger equation. We show that gradients act in a suitably chosen Sobolev space (Sobolev gradients) can be used in finite-difference and finite-element settings in a computationally efficient way to find minimum energy states of Schrödinger functionals. 相似文献
10.
The generic asymptotic behavior of a three-parameter weakly collapsing solution of a nonlinear Schrödinger equation is examined. A discrete set of zero-energy states is shown to exist. In the (A, C 1) parameter space, there are two close lines along which the amplitude of oscillating terms is exponentially small in the parameter C 1. 相似文献
11.
《Physics letters. A》2002,295(4):192-197
By introducing the concept of differential equations with “given curvature condition”, we show that the modified nonlinear Schrödinger equations for κ=1 and −1 are, respectively, gauge equivalent to the modified HF model and the modified M-HF model. As a consequence, soliton solutions to the modified HF model are constructed. 相似文献
12.
The nonlinear Schrödinger equation, known in low-temperature physics as the Gross-Pitaevskii equation, has a large family of excitations of different kinds. They include sound excitations, vortices, and solitons. The dynamics of vortices strictly depends on the separation between them. For large separations, some kind of adiabatic approximation can be used. We consider the case where an adiabatic approximation can be used (large separation between vortices) and the opposite case of a decay of the initial state, which is close to the double vortex solution. In the last problem, no adiabatic parameter exists (the interaction is strong). Nevertheless, a small numerical parameter arises in the problem of the decay rate, connected with an existence of a large centrifugal potential, which leads to a small value of the increment. The properties of the nonlinear wave equation are briefly considered in the Appendix A. 相似文献
13.
It was shown in a previous communication that the nonlinear Schrödinger equation exhibits a spectrum of eigenfunctions of the form = k,A
k
(coshkx)
–k
and = k
B
k
(coshkx)
–k–1sinhkx, and the corresponding eigenvalues of the energy are related to a band structure with a characteristic energy gap as a significant feature. In the present paper, it is shown that a further spectrum exists exhibiting the general structure =
k=0
A
k(cosh kx)–k–1/2and =
k=0
Bk(cosh kx)–k–3/2sinhkx and yielding also a band structure. An extension of the solution spectrum to a nonlinear Klein-Gordon equation and a nonlinear Dirac equation does not imply essential difficulties, and the corresponding characteristic band structure has to be related to a mass spectrum. 相似文献
14.
Three different types of chaotic behavior and instabilities (homoclinic chaos, hyperbolic resonance, and parabolic resonance) in Hamiltonian perturbations of the nonlinear Schr?dinger (NLS) equation are described. The analysis is performed on a truncated model using a novel framework in which a hierarchy of bifurcations is constructed. It is demonstrated numerically that the forced NLS equation exhibits analogous types of chaotic phenomena. Thus, by adjusting the forcing frequency, the behavior near the plane wave solution may be set to any one of the three different types of chaos for any periodic box length. 相似文献
15.
16.
A. M. Kosevich 《Journal of Experimental and Theoretical Physics》2001,92(5):866-870
Hamiltonian equations are formulated in terms of collective variables describing the dynamics of the soliton of an integrable nonlinear Schrödinger equation on a 1D lattice. Earlier, similar equations of motion were suggested for the soliton of the nonlinear Schrödinger equation in partial derivatives. The operator of soliton momentum in a discrete chain is defined; this operator is unambiguously related to the velocity of the center of gravity of the soliton. The resulting Hamiltonian equations are similar to those for the continuous nonlinear Schrödinger equation, but the role of the field momentum is played by the summed quasi-momentum of virtual elementary system excitations related to the soliton. 相似文献
17.
S. G. Chung 《Journal of statistical physics》1985,40(1-2):303-328
A fermionic perturbation theory is developed for the statistical mechanics of the nonlinear Schrödinger model. The theory is based on an interacting-fermion picture of the Bethe wave function. The inner product of the Bethe wave function is explicitly evaluated, and a simple graphical representation of it is given. The basic equations obtained for the free energy agree with those of Yang and Yang. In particular, the present theory gives a clear-cut meaning to the function of Yang and Yang: It represents a fermion energy at finite temperatures. 相似文献
18.
19.
F. Merle 《Communications in Mathematical Physics》1992,149(2):377-414
We consider the solutionu ?(t) of the saturated nonlinear Schrödinger equation
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