KDV equations
Approximate nonclassical symmetries for the time-fractional KdV equations with the small parameter
... In this paper, we applied the approximate nonclassical Lie symmetry analysis to a class of time-fractional differential equations with the small parameter. By employ- ing these method and some technical ...
8
Simulation of blow-up solutions to the generalized KdV equations by moving collocation methods
... From Tables and , we may see that the convergence rates for the conservative col- location methods are . The convergence order of the moving collocation method with fifth-order Hermite polynomial basis is expected to ...
17
Approximate Solution Method of the Seventh Order KdV Equations by Decomposition Method
... In this paper, Adomian decomposition method (ADM) is implemented to approximate the solution of the Korteweg-de Vries (KdV) equations of se- venth order, which are Kaup-Kuperschmidt equation and seventh ...
8
NEW ITERATIVE METHOD FOR SOLVING HIGHER ORDER KDV EQUATIONS
... In this paper, New Iterative Method has been successfully used for obtaining the analytic solutions for Lax equations and Sawada-Kotera KdV equations of fifth and seventh orders. NIM solutions are ...
12
Modified Adomain Decomposition Method for the Generalized Fifth Order KdV Equations
... generalized) KdV is the essential a model foe several physical phenomena including shal- low-water waves near critical value of surface tension and waves in nonlinear LC circuit with mutual induc- tance between ...
6
A Study on Exact Travelling Wave Solutions of Generalized KdV Equations
... classical KdV equation has been played a central role in the study of nonlinear phenomena, especially solitons phenomena which exist due to a balance between weak nonlinearity and ...fundamental equations ...
7
Formation of the dynamic energy cascades in quartic and quintic generalized KdV equations
... so-called B ENJAMIN –F EIR Index (BFI) [16], which characterizes the likelihood of freak wave formation in an open ocean, is also based on the effect of the MI in the presence of a fairly broad spectrum. There is a ...
20
Modifications of the Multistep Optimal Homotopy Asymptotic Method to Some Nonlinear KdV-Equations
... The mathematical theory of (MOHAM) provides highly accurate solutions for the system of BVP presented in section 3. We have used Mathematica 7 for our computational work. In Table 1-2, the (MOHAM) results are compared ...
16
Formation of the dynamic energy cascades in quartic and quintic generalized KdV equations
... Abstract: In this study we investigate the formation of dynamical energy cascades in higher order KdV-type equations. In the beginning we recall what is known about the dynamic cascades for the classical ...
21
Stability of solitonic solutions of Super KdV equations under susy breaking conditions
... Super KdV system and analyzed a solitonic model in terms of a Clifford algebra-valued ...of KdV equation and extended here for Clifford-valued fields may also be used in the stability analysis of ...
10
An Expansion Based on Sine-Gordon Equation to Solve KdV and modified KdV Equations in Conformable Fractional Forms
... the KdV equa- tion to determine periodic and soliton type wave solutions ...the KdV equation in vari- ous rational forms of hyperbolic or trigonometric function series ...
14
Lie symmetry analysis for Kawahara-KdV equations
... evolution equations (NLEEs) recently have been used to model many physical phenomena in various fields such as fluid mechanics, solid state physics, plasma physics, chemical physics, optical fiber and ...
11
ENERGY PRESERVING INTEGRATION OF KDV-KDV SYSTEMS
... coupled KdV equations (1) and (2), the integrals can be computed exactly and the computational cost is comparable with the symplectic Gauss-Legendre Runge-Kutta ...
9
Construction of \((n+1)\) dimensional dual mode nonlinear equations: multiple shock wave solutions for \((3+1)\) dimensional dual mode Gardner type and KdV type
... fifth-order KdV equations (TMFKdV) [14, 15], the two-mode higher-order Boussinesq–Burger system [16], two-mode coupled Burgers equation [17], two-mode coupled modified Korteweg– de Vries [18], two-mode ...
12
Exact Traveling Wave Solutions of Nonlinear PDEs in Mathematical Physics
... In this section, we apply the extended mapping method to construct the exact solutions for the variant Boussi- nesq equations and the coupled KdV equations. Which are very important nonlinear ...
8
Global Attractor of Two Dimensional Strong Damping KDV Equation and Its Dimension Estimation
... one-dimensional KDV equation and its ...dimensional KDV equations and its upper bound estimation of the Hausdorff and fractal dimension of ...
9
ΖN graded discrete Lax pairs and integrable difference equations
... In this paper we introduce an N × N spectral problem, linear in the spectral parameter and with Z N grading, which gives rise to a large class of discrete integrable systems. In the 2 × 2 specialisation, these include ...
31
Homotopy Perturbation Method for the Generalized Hirota Satsuma Coupled KdV Equation
... [62] E. M. E. Zayed, T. A. Nofal and K. A. Gepreel, “On Us- ing the Homotopy Perturbation Method for Finding the Travelling Wave Solutions of Generalized Nonlinear Hi- rota-Satsuma Coupled KdV Equations,” ...
7
Equivalence of the Open KdV and the Open Virasoro Equations for the Moduli Space of Riemann Surfaces with Boundary
... open KdV equations and the open Virasoro equations provide two different ways to describe the intersection numbers on the moduli space of Riemann surfaces with ...open KdV equations has ...
17
Quasi-periodic solutions for nonlinear wave equation with singular Legendre potential
... the KdV equations, Benjamin–Ono equations, derivative nonlinear Schrödinger equations and derivative nonlinear wave equations, the corresponding unbounded KAM theorems were developed to ...
18