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The matrix Lax representation of the generalized Riemann equations and its conservation Laws
generalized Riemann equation Saxton equation Lax representation
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2011/7/5
It is shown that the generalized Riemann equation is equivalent with the
multicomponent generalization of the Hunter - Saxton equation. New matrix
and scalar Lax representation is presented for this...
A Roe-type Riemann solver based on the spectral decomposition of the equations of Relativistic Magnetohydrodynamics
Roe-type Riemann solver spectral decomposition equations of Relativistic Magnetohydrodynamics
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2011/3/2
In a recent paper (Ant´on et al. 2010) we have derived sets of right and left eigenvectors of the Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any ...
Geometric transformations and soliton equations
Differential Geometry (math.DG) Exactly Solvable and Integrable Systems (nlin.SI)
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2010/11/11
We give a survey of the following six closely related topics: (i) a general method for constructing a soliton hierarchy from a splitting of a loop algebra into positive and negative subalgebras, toget...
Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations
Analysis of PDEs (math.AP) Exactly Solvable and Integrable Systems (nlin.SI)
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2010/11/11
We first review the known mathematical results concerning the KP type equations. Then we perform numerical simulations to analyze various qualitative properties of the equations : blow-up versus long ...
Reduction of Multidimensional Wave Equations to Two-Dimensional Equations: Investigation of Possible Reduced Equations
Mathematical Physics (math-ph) Analysis of PDEs (math.AP) Exactly Solvable and Integrable Systems (nlin.SI)
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2010/11/11
We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigati...
On nonclassical symmetries of generalized Huxley equations
contribution to the Proceedings of 5th Workshop "Group Analysis of Differential Equations and Integrable Systems" (4 - 10 June 2010, Protaras, Cyprus)
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2010/11/10
Nonclassical symmetries of a class of generalized Huxley equations of form $u_t=u_{xx}+k(x)u^2(1-u)$ are found. More precisely, for the class under consideration we completely classify reduction opera...
Integrable Origins of Higher Order Painleve Equations
Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics (math-ph)
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2010/11/10
Higher order Painleve equations invariant under extended affine Weyl groups $A^{(1)}_n$ are obtained through self-similarity limit of a class of pseudo-differential Lax hierarchies with symmetry inher...
Non-uniform continuity of periodic Holm-Staley b-family of equations
Exactly Solvable and Integrable Systems (nlin.SI)
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2010/11/10
We consider a family of non-evolutionary partial differential equations known as Holm - Staley b - family which includes the integrable Camassa-Holm and Degasperis-Procesi equations. We show that the ...
Integrability Test for Discrete Equations via Generalized Symmetries
Exactly Solvable and Integrable Systems (nlin.SI)
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2010/11/10
In this article we present some integrability conditions for partial difference equations obtained using the formal symmetries approach. We apply them to find integrable partial difference equations c...
A multiple exp-function method for nonlinear differential equations and its application
Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics (math-ph)
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2010/11/10
A multiple exp-function method to exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards ease of use and capability of computer algebra s...
The lattice structure of connection preserving deformations for q-Painleve equations I
Exactly Solvable and Integrable Systems (nlin.SI)
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2010/11/10
We wish to explore a link between the Lax integrability of the q-Painleve equations and the symmetries of the q-Painleve equations. To do this, we consider the set of associated linear problems for th...
Reduction operators of variable coefficient semilinear diffusion equations with an exponential source
Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics (math-ph)
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2010/11/10
Reduction operators (called also nonclassical or $Q$-conditional symmetries) of variable coefficient semilinear reaction-diffusion equations with exponential source $f(x)u_t=(g(x)u_x)_x+h(x)e^{mu}$ ar...
The Schwarzian variable associated with discrete KdV-type equations
Exactly Solvable and Integrable Systems (nlin.SI)
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2010/11/10
We present a new construction related to systems of polynomials which are consistent on a cube. The consistent polynomials underlie the integrability of discrete counterparts of integrable partial dif...
Symmetry classification of third-order nonlinear evolution equations. Part I: Semi-simple algebras
Exactly Solvable and Integrable Systems(nlin.SI) Mathematical Physics(math-ph)
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2010/11/10
We give a complete point-symmetry classification of all third-order evolution equations of the form $u_t=F(t,x,u,u_x, u_{xx})u_{xxx}+G(t,x,u,u_x, u_{xx})$ which admit semi-simple symmetry algebras and...