共查询到20条相似文献,搜索用时 13 毫秒
1.
Yong Chen Biao Li Hongqing Zhang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,53(4):983-993
Making use of a proper transformation and a generalized ansatz, we consider a new generalized Hamiltonian amplitude equation with nonlinear terms of any order, iux + utt + (|u|p + |u|2p)u + uxt = 0. As a result, many explicit exact solutions, which include kink-shaped soliton solutions, bell-shaped soliton solutions, periodic wave solutions, the combined formal solitary wave solutions and rational solutions, are obtained. 相似文献
2.
The aim of this paper is to study the qualitative behavior of large solutions to the following problem
3.
In this paper we study the boundary behavior of solutions to equations of the form
∇⋅A(x,∇u)+B(x,∇u)=0, 相似文献
4.
Zhijun Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(10):3348-3363
In this paper, we study the boundary behavior of solutions to boundary blow-up elliptic problems , where Ω is a bounded domain with smooth boundary in RN, q>0, , which is positive in Ω and may be vanishing on the boundary and rapidly varying near the boundary, and f is rapidly varying or normalized regularly varying at infinity. 相似文献
5.
Jinmyoung Seok 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(12):4252-4259
For the following elliptic system in R3
6.
7.
8.
In this paper, one-dimensional (1D) nonlinear Schrödinger equation
iut−uxx+mu+4|u|u=0 相似文献
9.
We study the existence of periodic solutions for a second order non-autonomous dynamical system containing variable kinetic energy terms. Our assumptions balance the interaction between the kinetic energy and the potential energy with neither one dominating the other. We study sublinear problems and the existence of non-constant solutions. 相似文献
10.
11.
12.
X. Carvajal 《Journal of Differential Equations》2010,249(9):2214-2236
Applying an Abstract Interpolation Lemma, we showed persistence of solutions of the initial value problem to higher order nonlinear Schrödinger equation, also called Airy-Schrödinger equation, in weighted Sobolev spaces X2,θ, for θ∈[0,1]. 相似文献
13.
Amin Esfahani 《Journal of Differential Equations》2009,247(12):3181-323
In this paper we study the generalized BO-ZK equation in two space dimensions
ut+upux+αHuxx+εuxyy=0. 相似文献
14.
Jie Ji 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):4034-4046
In this paper, the bilinear form of a negative order non-isospectral AKNS equation is given. The soliton solutions are obtained through Hirota’s direct method and the Wronskian technique, respectively. 相似文献
15.
A generalization of the Camassa-Holm equation, a model for shallow water waves, is investigated. Using the pseudoparabolic regularization technique, its local well-posedness in Sobolev space Hs(R) with is established via a limiting procedure. In addition, a sufficient condition for the existence of weak solutions of the equation in lower order Sobolev space Hs with is developed. 相似文献
16.
Franco Obersnel 《Journal of Differential Equations》2010,249(7):1674-1725
We discuss existence and multiplicity of positive solutions of the prescribed mean curvature problem
17.
18.
We study the nonlinear self-adjointness of a general class of quasilinear 2D second order evolution equations which do not possess variational structure. For this purpose, we use the method of Ibragimov, devised and developed recently. This approach enables one to establish the conservation laws for any differential equation. We first obtain conditions determining the self-adjoint sub-class in the general case. Then, we establish the conservation laws for important particular cases: the Ricci Flow equation, the modified Ricci Flow equation and the nonlinear heat equation. 相似文献
19.
The existence of global weak solutions for a generalized Benjamin-Bona-MahonyBurgers equation is established in the space C([0, ∞) × R) ∩ L~∞([0, ∞); H1(R)) under the condition that its initial value belongs to the space H1(R). A one-sided super bound estimate and a space-time higher-norm estimate on the first order derivatives of the solution with respect to the space variable are derived to prove the existence. 相似文献
20.
Shaoyong Lai 《Journal of Computational and Applied Mathematics》2009,231(1):311-318
A technique based on the reduction of order for solving differential equations is employed to investigate a generalized nonlinear Boussinesq wave equation. The compacton solutions, solitons, solitary pattern solutions, periodic solutions and algebraic travelling wave solutions for the equation are expressed analytically under several circumstances. The qualitative change in the physical structures of the solutions is highlighted. 相似文献