Results 11 to 20 of about 2,203 (128)
QUASIINVARIANT GAUSSIAN MEASURES FOR ONE-DIMENSIONAL HAMILTONIAN PARTIAL DIFFERENTIAL EQUATIONS
Forum of Mathematics, Sigma, 2015 We prove the quasiinvariance of Gaussian measures (supported by functions of increasing Sobolev regularity) under the flow of one-dimensional Hamiltonian partial differential equations such as the regularized long wave, also
NIKOLAY TZVETKOV
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Lump and Interaction Solutions of Linear PDEs in (3 + 1)-Dimensions
East Asian Journal on Applied Mathematics, 2019 Linear partial differential equations in (3 + 1)-dimensions consisting of all mixed second-order derivatives are considered, and Maple symbolic computations are made to construct their lump and interaction solutions, including lump-periodic, lumpkink and
W. Ma
semanticscholar +1 more source
An efficient approach for the numerical solution of fifth-order KdV equations
Open Mathematics, 2020 The main aim of this article is to use a new and simple algorithm namely the modified variational iteration algorithm-II (MVIA-II) to obtain numerical solutions of different types of fifth-order Korteweg-de Vries (KdV) equations.
Ahmad Hijaz +2 more
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Optimal control of a viscous generalized θ-type dispersive equation with weak dissipation
Open Mathematics, 2020 In this paper, we investigate the problem for optimal control of a viscous generalized θ\theta -type dispersive equation (VG θ\theta -type DE) with weak dissipation. First, we prove the existence and uniqueness of weak solution to the equation.
Fan Guobing, Yang Zhifeng
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Gardner's deformations of the graded Korteweg-de Vries equations revisited [PDF]
J.Math.Phys. 53:10 (2012) 103511, 18p, 2011 We solve the Gardner deformation problem for the N=2 supersymmetric a=4 Korteweg-de Vries equation (P. Mathieu, 1988). We show that a known zero-curvature representation for this superequation yields the system of new nonlocal variables such that their derivatives contain the Gardner deformation for the classical KdV equation.
arxiv +1 more source
A LIPSCHITZ METRIC FOR THE CAMASSA–HOLM EQUATION
Forum of Mathematics, Sigma, 2020 We analyze stability of conservative solutions of the Cauchy problem on the line for the Camassa–Holm (CH) equation. Generically, the solutions of the CH equation develop singularities with steep gradients while preserving continuity of the solution ...
JOSÉ A. CARRILLO +2 more
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Controlling the dynamics of Burgers equation with a high‐order nonlinearity
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 62, Page 3321-3332, 2004., 2004 We investigate analytically as well as numerically Burgers equation with a high‐order nonlinearity (i.e., ut = νuxx − unux + mu + h(x)). We show existence of an absorbing ball in L2[0, 1] and uniqueness of steady state solutions for all integer n ≥ 1.
Nejib Smaoui
wiley +1 more source
Bi-integrable and tri-integrable couplings of a soliton hierarchy associated with SO(4)
Open Mathematics, 2017 In our paper, the theory of bi-integrable and tri-integrable couplings is generalized to the discrete case. First, based on the six-dimensional real special orthogonal Lie algebra SO(4), we construct bi-integrable and tri-integrable couplings associated ...
Zhang Jian, Zhang Chiping, Cui Yunan
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East Asian Journal on Applied Mathematics, 2019 The (3 + 1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation is studied by using the Hirota bilinear method and the graphical representations of the solutions.
Ding Guo +3 more
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The generalized Burgers equation with and without a time delay
International Journal of Stochastic Analysis, Volume 2004, Issue 1, Page 73-96, 2004., 2004 We consider the generalized Burgers equation with and without a time delay when the boundary conditions are periodic with period 2π. For the generalized Burgers equation without a time delay, that is, ut = vuxx − uux + u + h(x), 0 < x < 2π, t > 0, u(0, t) = u(2π, t), u(x, 0) = u0(x), a Lyapunov function method is used to show boundedness and uniqueness
Nejib Smaoui, Mona Mekkaoui
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