Results 11 to 20 of about 2,219 (128)
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
doaj +1 more source
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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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
The geometric sense of R. Sasaki connection [PDF]
, 2002 For the Riemannian manifold $M^{n}$ two special connections on the sum of the tangent bundle $TM^{n}$ and the trivial one-dimensional bundle are constructed. These connections are flat if and only if the space $M^{n}$ has a constant sectional curvature $\
Alexey V Shchepetilov +9 more
core +4 more sources
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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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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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
semanticscholar +1 more source
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
Resonance-based schemes for dispersive equations via decorated trees
Forum of Mathematics, Pi, 2022 We introduce a numerical framework for dispersive equations embedding their underlying resonance structure into the discretisation. This will allow us to resolve the nonlinear oscillations of the partial differential equation (PDE) and to approximate ...
Yvain Bruned, Katharina Schratz
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