Elliptic general analytic solutions
Robert Conte,Micheline Musette +1 more
TLDR
In this paper, the authors present an algorithm able to find all traveling waves which are elliptic or degenerate elliptic, i.e. rational in one exponential or rational.Abstract:
In order to find analytically the travelling waves of partially integrable autonomous nonlinear partial differential equations, many methods have been proposed over the ages: "projective Riccati method", "tanh-method", "exponential method", "Jacobi expansion method", "new ...", etc. The common default to all these "truncation methods" is to only provide some solutions, not all of them. By implementing three classical results of Briot, Bouquet and Poincare', we present an algorithm able to provide in closed form \textit{all} those travellingz waves which are elliptic or degenerate elliptic, i.e. rational in one exponential or rational. Our examples here include the Kuramoto-Sivashinsky equation and the cubic and quintic complex Ginzburg-Landau equations.read more
Citations
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Correlation of financial markets in times of crisis
TL;DR: In this paper, the eigenvalues and eigenvectors of correlations matrices of some of the main financial market indices in the world were used to investigate financial market crises that occurred in the years 1987 (Black Monday), 1998 (Russian crisis), 2001 (Burst of the dot-com bubble and September 11), and 2008 (Subprime Mortgage Crisis).
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Optical Soliton Solutions of the Cubic-Quartic Nonlinear Schrödinger and Resonant Nonlinear Schrödinger Equation with the Parabolic Law
TL;DR: In this paper, the cubic-quartic nonlinear Schrodinger and resonant nonsmrodinger equation in parabolic law media are investigated to obtain the dark, singular, bright-singular combo and periodic soliton solutions.
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Novel Complex Wave Solutions of the (2+1)-Dimensional Hyperbolic Nonlinear Schrödinger Equation
TL;DR: In this article, the application of the (m+1/G′)-expansion method to the (2+1)-dimensional hyperbolic nonlinear Schrodinger equation is discussed.
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On integrability of nonautonomous nonlinear Schrödinger equations
TL;DR: In this article, the authors show how to transform the nonautonomous nonlinear Schroedinger equation with quadratic Hamiltonians into the standard autonomous form that is completely integrable by the familiar inverse scattering method in nonlinear science.
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Pruning a minimum spanning tree
TL;DR: This work employs various techniques in order to filter random noise from the information provided by minimum spanning trees obtained from the correlation matrices of international stock market indices prior to and during times of crisis.
References
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Book
Solitons, Nonlinear Evolution Equations and Inverse Scattering
M. A. Ablowitz,Peter A. Clarkson +1 more
TL;DR: In this article, the authors bring together several aspects of soliton theory currently only available in research papers, including inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multidimensional space, and the ∂ method.
Book
Solitons and the Inverse Scattering Transform
Mark J. Ablowitz,Harvey Segur +1 more
TL;DR: In this paper, the authors developed the theory of the inverse scattering transform (IST) for ocean wave evolution, which can be solved exactly by the soliton solution of the Korteweg-deVries equation.
Journal ArticleDOI
The Painlevé property for partial differential equations
TL;DR: In this paper, the authors define the Painleve property for partial differential equations and show how it determines, in a remarkably simple manner, the integrability, the Backlund transforms, the linearizing transforms, and the Lax pairs of three well-known partial differential equation (Burgers' equation, KdV equation, and modified KDV equation).
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Persistent Propagation of Concentration Waves in Dissipative Media Far from Thermal Equilibrium
Yoshiki Kuramoto,Toshio Tsuzuki +1 more
TL;DR: In this paper, the origin of persistent wave propagation through medium of reactwn-diffusion type 1s is explored based on a generalized time-dependent Ginzburg-Landau equation for a complex field W, namely, the equation derived previously in connection with the instability problems in nonlinear chemical kinetics.
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Front propagation into unstable states
TL;DR: In this paper, the authors present an introductory review of the problem of front propagation into unstable states, which is centered around the concept of the asymptotic linear spreading velocity v ∗, the rate with which initially localized perturbations spread into an unstable state according to the linear dynamical equations obtained by linearizing the fully nonlinear equations about the unstable state.