Results 11 to 20 of about 1,133 (78)
Proceedings of the London Mathematical Society, Volume 121, Issue 4, Page 954-1032, October 2020., 2020 Abstract I provide an explicit construction of spectral curves for the affine E8 relativistic Toda chain. Their closed‐form expression is obtained by determining the full set of character relations in the representation ring of E8 for the exterior algebra of the adjoint representation; this is in turn employed to provide an explicit construction of ...
Andrea Brini
wiley +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
doaj +1 more source
Restricted Flows and the Soliton Equation with Self-Consistent Sources [PDF]
, 2006 The KdV equation is used as an example to illustrate the relation between the restricted flows and the soliton equation with self-consistent sources. Inspired by the results on the Backlund transformation for the restricted flows (by V.B. Kuznetsov et al.
Lin, Runliang, Yao, Haishen, Zeng, Yunbo
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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On the Cauchy Problem for the modified Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data [PDF]
, 2010 We solve the Cauchy problem for the modified Korteweg--de Vries equation with steplike quasi-periodic, finite-gap initial conditions under the assumption that the perturbations have a given number of derivatives and moments finite.Comment: 8 ...
Egorova, Iryna, Teschl, Gerald
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Alexandria Engineering Journal, 2020 The present paper employs the space-time fractional nonlinear Bogoyavlenskii equation and Schrodinger equation. We perform a new method to take some new solitary wave phenomena for each equation.
Md Nur Alam, Cemil Tunç
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On the Virasoro Structure of Symmetry Algebras of Nonlinear Partial Differential Equations [PDF]
, 2006 We discuss Lie algebras of the Lie symmetry groups of two generically non-integrable equations in one temporal and two space dimensions arising in different contexts.
Gungor, Faruk
core +4 more sources
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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