共查询到20条相似文献,搜索用时 31 毫秒
1.
We consider solitary-wave solutions of the generalized regularized long-wave (RLW) and Korteweg-de Vries (KdV) equations. We prove the convergence of Adomian decomposition method applied to the generalized RLW and KdV equations. Then we obtain the exact solitary-wave solutions and numerical solutions of the generalized RLW and KdV equations for the initial conditions. The numerical solutions are compared with the known analytical solutions. Their remarkable accuracy are finally demonstrated for the generalized RLW and KdV equations. 相似文献
2.
This paper studies the approximation of solutions for the incompressible convective Brinkman–Forchheimer (CBF) equations via the artificial compressibility method. We first introduce a family of perturbed compressible CBF equations that approximate the incompressible CBF equations. Then, we prove the existence and convergence of solutions for the compressible CBF equations to the solutions of the incompressible CBF equations. 相似文献
3.
K. M. Tamizhmani A. Ramani T. Tamizhmani B. Grammaticos 《Journal of Computational and Applied Mathematics》2003,160(1-2):307-313
We present results on special solutions of discrete Painlevé equations. These solutions exist only when one constraint among the parameters of the equation is satisfied and are obtained through the solutions of linear second-order (discrete) equations. These linear equations define the discrete analogues of special functions. 相似文献
4.
We study the regularity criteria for weak solutions to the incompressible magnetohydrodynamic equations. Some regularity criteria are obtained for weak solutions to the magnetohydrodynamic equations, which generalize the results in [C. He, Z. Xin, On the regularity of solutions to the magneto-hydrodynamic equations, J. Differential Equations 213 (2) (2005) 235-254]. Our results reveal that the velocity field of the fluid plays a more dominant role than the magnetic field does on the regularity of solutions to the magnetohydrodynamic equations. 相似文献
5.
Timothy Michael Deis 《Semigroup Forum》2006,73(2):194-206
We prove that finding solutions to the class of single multilinear equations in FIM(A) is decidable; while finding solutions
to the class of systems of multilinear equations in FIM(A) is undecidable. 相似文献
6.
A. H. Bhrawy Anjan Biswas M. Javidi Wen Xiu Ma Zehra Pınar Ahmet Yıldırım 《Results in Mathematics》2013,63(1-2):675-686
In this paper, using the exp-function method we obtain some new exact solutions for (1+1)-dimensional and (2+1)-dimensional Kaup–Kupershmidt (KK) equations. We show figures of some of the new solutions obtained here. We conclude that the exp-function method presents a wider applicability for handling nonlinear partial differential equations. 相似文献
7.
We study Hessian fully nonlinear uniformly elliptic equations and show that the second derivatives of viscosity solutions of those equations (in 12 or more dimensions) can blow up in an interior point of the domain. We prove that the optimal interior regularity of such solutions is no more than C1+?, showing the optimality of the known interior regularity result. The same is proven for Isaacs equations. We prove the existence of non-smooth solutions to fully nonlinear Hessian uniformly elliptic equations in 11 dimensions. We study also the possible singularity of solutions of Hessian equations defined in a neighborhood of a point and prove that a homogeneous order 0<α<1 solution of a Hessian uniformly elliptic equation in a punctured ball should be radial. 相似文献
8.
《随机分析与应用》2013,31(6):1281-1307
The paper is devoted to the generalized stochastic differential equations of the Ito? type whose coefficients are additionally perturbed and dependent on a small parameter. Their solutions are compared with the solutions of the corresponding unperturbed equations. We give conditions under which the solutions of these equations are close in the (2m)-th moment sense on finite intervals or on intervals whose length tends to infinity as the small parameter tends to zero. We also give the degree of the closeness of these solutions. 相似文献
9.
In previous article [M. Zhan, Phase-lock equations and its connections to Ginzburg–Landau equations of superconductivity, J. Nonlinear Anal. 42 (2000) 1063–1075], we introduced a system of equations (phase-lock equations) to model the superconductivity phenomena. We investigated its connection to Ginzburg–Landau equations and proved the existence and uniqueness of both weak and strong solutions. In this article, we study the steady-state problem associated with the phase-lock equations. We prove that the steady-state problem has multiple solutions and show that the solution set enjoys some structural properties as proved by Foias and Teman for the Navier–Stokes equations in [C. Foias, R. Teman, Structure of the set of stationary solutions of the Navier–Stokes equations, Commun. Pure Appl. Math. XXX (1977) 149–164]. 相似文献
10.
We prove a large deviation principle result for solutions of abstract stochastic evolution equations perturbed by small Lévy noise. We use general large deviations theorems of Varadhan and Bryc coupled with the techniques of Feng and Kurtz (2006) [15], viscosity solutions of integro-partial differential equations in Hilbert spaces, and deterministic optimal control methods. The Laplace limit is identified as a viscosity solution of a Hamilton-Jacobi-Bellman equation of an associated control problem. We also establish exponential moment estimates for solutions of stochastic evolution equations driven by Lévy noise. General results are applied to stochastic hyperbolic equations perturbed by subordinated Wiener process. 相似文献
11.
Asymptotic Solutions of Nonrelativistic Equations of Quantum Mechanics in Curved Nanotubes: I. Reduction to Spatially One-Dimensional Equations 总被引:1,自引:0,他引:1
Belov V. V. Dobrokhotov S. Yu. Tudorovskii T. Ya. 《Theoretical and Mathematical Physics》2004,141(2):1562-1592
We consider equations of nonrelativistic quantum mechanics in thin three-dimensional tubes (nanotubes). We suggest a version of the adiabatic approximation that permits reducing the original three-dimensional equations to one-dimensional equations for a wide range of energies of longitudinal motion. The suggested reduction method (the operator method for separating the variables) is based on the Maslov operator method. We classify the solutions of the reduced one-dimensional equation. In Part I of this paper, we deal with the reduction problem, consider the main ideas of the operator separation of variables (in the adiabatic approximation), and derive the reduced equations. In Part II, we will discuss various asymptotic solutions and several effects described by these solutions. 相似文献
12.
K. A. Volosov 《Journal of Applied and Industrial Mathematics》2009,3(4):519-527
We propose a method for constructing solutions to a class of quasilinear parabolic partial differential equations (PDEs) basing
on a new property of these equations. The method applies to quasilinear hyperbolic and elliptic equations as well. The results
of this article broaden the class of exact solutions to the quasilinear equations, in particular, to the nonlinear heat equations,
the equations of chemical kinetics and mathematical biology. 相似文献
13.
T. Hayat I. Naeem M. Ayub A.M. Siddiqui S. Asghar C.M. Khalique 《Nonlinear Analysis: Real World Applications》2009,10(4):2117-2126
We present here the exact solutions for the equations of magnetohydrodynamic (MHD) aligned flow of a second grade fluid. The exact solutions are constructed for steady and unsteady equations by employing inverse method. 相似文献
14.
马文秀 《数学物理学报(B辑英文版)》2019,(2)
Taking a class of linear(4+1)-dimensional partial differential equations as examples, we would like to show that there exist lump solutions and interaction solutions in(4+1)-dimensions. We will compute abundant lump solutions and interaction solutions to the considered linear(4+1)-dimensional partial differential equations via symbolic computations,and plot three specific solutions with Maple plot tools, which supplements the existing literature on lump, rogue wave and breather solutions and their interaction solutions in soliton theory. 相似文献
15.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(6):1746-1769
In this paper we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a recently-derived integrable family of generalized Camassa–Holm (GCH) equations. A recent, novel application of phase-plane analysis is employed to analyze the singular traveling wave equations of three of the GCH NLPDEs, i.e. the possible non-smooth peakon and cuspon solutions. One of the considered GCH equations supports both solitary (peakon) and periodic (cuspon) cusp waves in different parameter regimes. The second equation does not support singular traveling waves and the last one supports four-segmented, non-smooth M-wave solutions.Moreover, smooth traveling waves of the three GCH equations are considered. Here, we use a recent technique to derive convergent multi-infinite series solutions for the homoclinic orbits of their traveling-wave equations, corresponding to pulse (kink or shock) solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddle equilibrium points of the corresponding GCH equations, as well as ensure simultaneous convergence and continuity of the multi-infinite series solutions for the homoclinic orbits anchored by these saddle points. Unlike the majority of unaccelerated convergent series, high accuracy is attained with relatively few terms. We also show the traveling wave nature of these pulse and front solutions to the GCH NLPDEs. 相似文献
16.
V. I. Zhegalov 《Differential Equations》2008,44(7):900-908
We consider Volterra partial differential equations with two and three independent variables and reduce them to Goursat problems, whose solutions are constructed by the Riemann method. We single out cases in which the corresponding Riemann functions (and hence the solutions of the original equations) can be written out in closed form. 相似文献
17.
We consider a coupled van der Pol equation system. Our coupled system consists of two van der Pol equations that are connected
with each other by linear terms. We assume that two distinctive solutions (out-of-phase and in-phase solutions) exist in the
dynamical system of coupled equations and give answers to some problems. 相似文献
18.
Classifying Integrable Egoroff Hydrodynamic Chains 总被引:1,自引:0,他引:1
We introduce the notion of Egoroff hydrodynamic chains. We show how they are related to integrable (2+1)-dimensional equations of hydrodynamic type. We classify these equations in the simplest case. We find (2+1)-dimensional equations that are not just generalizations of the already known Khokhlov–Zabolotskaya and Boyer–Finley equations but are much more involved. These equations are parameterized by theta functions and by solutions of the Chazy equations. We obtain analogues of the dispersionless Hirota equations. 相似文献
19.
We build spaces of q.p. (quasi-periodic) functions and we establish some of their properties. They are motivated by the Percival approach to q.p. solutions of Hamiltonian systems. The periodic solutions of an adequatez partial differential equation are related to the q.p. solutions of an ordinary differential equation. We use this approach to obtain some regularization theorems of weak q.p. solutions of differential equations. For a large class of differential equations, the first theorem gives a result of density: a particular form of perturbated equations have strong solutions. The second theorem gives a condition which ensures that any essentially bounded weak solution is a strong one. 相似文献