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11.
Jochen Denzler 《Transactions of the American Mathematical Society》1997,349(10):4053-4083
It is shown that for an interesting class of perturbation functions, at most one of the continuum of sine-Gordon breathers can persist for the perturbed equation. This question is much more subtle than the question of persistence of large portions of the family, because analytic continuation arguments in the amplitude parameter are no longer available. Instead, an asymptotic analysis of the obstructions to persistence for large Fourier orders is made, and it is connected to the asymptotic behaviour of the Taylor coefficients of the perturbation function by means of an inverse Laplace transform and an integral transform whose kernel involves hypergeometric functions in a way that is degenerate in that asymptotic analysis involves a splitting monkey saddle. Only first order perturbation theory enters into the argument. The reasoning can in principle be carried over to other perturbation functions than the ones considered here.
12.
X. R. Ma 《Proceedings of the American Mathematical Society》2005,133(11):3179-3189
We present a necessary and sufficient condition for two matrices given by two bivariate functions to be inverse to each other with certainty in the cases of Krattenthaler formula and Warnaar's elliptic matrix inversion. Immediate consequences of our result are some known functions and a constructive approach to derive new matrix inversions from known ones.
13.
Bi-solitons, breather solution family and rogue waves for the (2+1)-dimensional nonlinear Schr\"{o}dinger equation 下载免费PDF全文
Changfu Liu Min Chen Ping Zhou Longwei Chen 《Journal of Applied Analysis & Computation》2016,6(2):367-375
In this paper, bi-solitons, breather solution family and rogue
waves for the (2+1)-Dimensional nonlinear Schr\"{o}dinger equations
are obtained by using Exp-function method. These solutions derived
from one unified formula which is solution of the standard (1+1)
dimension nonlinear Schr\"{o}dinger equation. Further, based on the
solution obtained by other authors, higher-order rational rogue wave
solution are obtained by using the similarity transformation. These
results greatly enriched the diversity of wave structures for the
(2+1)-dimensional nonlinear Schr\"{o}dinger equations 相似文献
14.
引入中心对称向量和中心反对称向量的概念,证明数域P上任意n维向量都可以唯一地表示成一个中心对称向量和一个中心反对称向量的和;给出数域P上Skew对称矩阵的概念,并讨论其性质. 相似文献
15.
The effect of liquid on the propagation of waves in a micropolar elastic layer with stretch has been investigated. The frequency
and wave velocity equations for symmetric and antisymmetric vibrations are derived. Propagation of monochromatic waves in
a micropolar elastic layer with stretch is discussed. Results of this analysis reduce to those without stretch. 相似文献
16.
A variable-coefficient coupled nonlinear Schrödinger equation in an averaged dispersion-managed birefringent fiber is investigated. Based on the one-to-one correspondence between variable-coefficient and constant-coefficient equations, an analytical breather solution is derived. As an example to exhibit dynamical behaviors of solution, its controllable excitations including rear excitation, peak excitation and initial excitation are discussed. 相似文献
17.
For a one (2+1)-dimensional combined Kadomtsev-Petviashvili with its hierarchy equation, the missing D'Alembert type solution is derived first through the traveling wave transformation which contains several special kink molecule structures. Further, after introducing the Bäcklund transformation and an auxiliary variable, the N-soliton solution which contains some soliton molecules for this equation, is presented through its Hirota bilinear form. The concrete molecules including line solitons, breathers and a lump as well as several interactions of their hybrid are shown with the aid of special conditions and parameters. All these dynamical features are demonstrated through the different figures. 相似文献
18.
We investigate a (2+1)-dimensional shallow water wave equation and describe its nonlinear dynamical behaviors in physics. Based on the N-soliton solutions, the higher-order fissionable and fusionable waves, fissionable or fusionable waves mixed with soliton molecular and breather waves can be obtained by various constraints of special parameters. At the same time, by the long wave limit method, the interaction waves between fissionable or fusionable waves with higher-order lumps are acquired. Combined with the dynamic figures of the waves, the properties of the solution are deeply studied to reveal the physical significance of the waves. 相似文献
19.
20.
The (2+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation is an important integrable model. In this paper, we obtain the breather molecule, the breather-soliton molecule and some localized interaction solutions to the BLMP equation. In particular, by employing a compound method consisting of the velocity resonance, partial module resonance and degeneration of the breather techniques, we derive some interesting hybrid solutions mixed by a breather-soliton molecule/breather molecule and a lump, as well as a bell-shaped soliton and lump. Due to the lack of the long wave limit, it is the first time using the compound degeneration method to construct the hybrid solutions involving a lump. The dynamical behaviors and mathematical features of the solutions are analyzed theoretically and graphically. The method introduced can be effectively used to study the wave solutions of other nonlinear partial differential equations. 相似文献