Regular and Singular Pulse and Front Solutions and Possible Isochronous Behavior in the Short-Pulse Equation: Phase-Plane, Multi-Infinite Series and Variational Approaches [PDF]
, 2014 In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE).
Choudhury, A. Ghose +4 more
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On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation [PDF]
, 2004 The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations.
Bluman G. W. +14 more
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Topology, rigid cosymmetries and linearization instability in higher gauge theories [PDF]
, 2013 We consider a class of non-linear PDE systems, whose equations possess Noether identities (the equations are redundant), including non-variational systems (not coming from Lagrangian field theories), where Noether identities and infinitesimal gauge ...
Khavkine, Igor
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BSDE and generalized Dirichlet forms: the finite dimensional case [PDF]
, 2012 We consider the following quasi-linear parabolic system of backward partial differential equations: $(\partial_t+L)u+f(\cdot,\cdot,u, \nabla u\sigma)=0$ on $[0,T]\times \mathbb{R}^d\qquad u_T=\phi$, where $L$ is a possibly degenerate second order ...
Zhu, Rongchan
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Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system [PDF]
, 2019 This manuscript extends the analysis of a much studied singularly perturbed three-component reaction-diffusion system for front dynamics in the regime where the essential spectrum is close to the origin.
Chirilus-Bruckner, Martina +3 more
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Dispersionless integrable systems in 3D and Einstein-Weyl geometry [PDF]
, 2013 For several classes of second order dispersionless PDEs, we show that the symbols of their formal linearizations define conformal structures which must be Einstein-Weyl in 3D (or self-dual in 4D) if and only if the PDE is integrable by the method of ...
Ferapontov, Eugene, Kruglikov, Boris
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Nonlinear Waves: An Introduction [PDF]
, 2010 This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation, conservation laws equations and others ...
Popivanov, Petar, Slavova, Angela
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, 2010 In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical result by J.L. Lions for monotone operators. In particular,
Beyn +36 more
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, 2011 Following the previous works on the A. Pr\'astaro's formulation of algebraic topology of quantum (super) PDE's, it is proved that a canonical Heyting algebra ({\em integral Heyting algebra}) can be associated to any quantum PDE.
Prástaro, Agostino
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Flow-plate interactions: Well-posedness and long-time behavior [PDF]
, 2013 We consider flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are treated with Neumann type flow conditions, and a novel treatment ...
Chueshov, Igor +2 more
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