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A novel computational approach to the local fractional Lonngren wave equation in fractal media
The main purpose of this paper is to investigate the local fractional Lonngren wave equation, which is a generalization of Lonngren wave equation in...
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Abundant Resonant Behaviors of Soliton Solutions to the (3+1)-dimensional BKP-Boussinesq Equation
Resonant phenomena have been observed and investigated in various situations, such as plasma experiments, the maritime security and the microtubule...
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Exact Solutions of the Precursor Film Equation
We find and analyze exact solutions to equations with logarithmic nonlinearity. To construct the soltuions, we use the classical group analysis...
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Global solvability of initial boundary-value problems for nonlinear analogs of the Boussinesq equation
The solvability of the natural (first, second, and mixed) initial boundary-value problems for nonlinear analogs of the Boussinesq equation is...
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The General Noncompact Symmetric Space
From The Hitchhiker’s Guide to the Galaxy, by Douglas Adams, Pocket Books, NY, 1981. Reprinted by permission of The Crown Publishing Group.
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A new periodic solution to Jacobi elliptic functions of MKdV equation and BBM equation
Based on the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation...
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The Poincaré Upper Half-Plane
In Chap. 2, we considered a model for elliptic geometry, in which any two geodesics intersect, so that there are no parallels. Now we want to...
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Mixed problem for the equation governing inertia-gravity waves in the Boussinesq approximation in a unbounded cylindrical domain
The unique solvability of an initial-boundary value problem for the equation governing inertia-gravity waves in the Boussinesq approximation in an...
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On the numerical solution of quasilinear wave equation with strong dissipative term
The numerical solution for a type of quasilinear wave equation is studied. The three-level difference scheme for quasi-linear waver equation with...
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Modified Ginzburg–Landau Equation and Benjamin–Feir Instability
In this paper, a modulated wave train in a nonlinear monoinductance LC circuit is studied. Using the method of multiple scales in the general form,...
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Control of Chaos: Methods and Applications. II. Applications
Reviewed were the problems and methods for control of chaos, which in the last decade was the subject of intensive studies. Consideration was given...
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Envelope Modulational Instability in a Nonlinear Dissipative Transmission Line
A bi-inductance LC circuit is considered, and the envelope modulation is reduced to the complex nonlinear Schrödinger (CNLS) equation. The...
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Effect of a Localized Random Forcing Term on the Korteweg-De Vries Equation
In this work, we numerically investigate the influence of a white noise-type forcing on the phenomenon of forced generation of solitons by a...
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Applications of KdV
The discovery of the remarkable interaction properties of solitary wave solutions to KdV by Zabusky and Kruskal [62] and the invention by Gardner,...
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Nonelliptic Schrödinger equations
Nonelliptic Schrödinger equations are defined as multidimensional nonlinear dispersive wave equations whose linear part in the space variables is not...
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Sine-Gordon and Nonlinear Schrödinger
The sine-Gordon equation is a very important partial differential equation not only in the modern theory of condensed matter physics but also in many...
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Similarity solutions for nonlinear diffusion — a new integration procedure
The nonlinear diffusion equation arises in many important areas of science and technology and most of the known exact solutions turn out to be...
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Modified Kadometsev-Petviashvili equation for ion-acoustic waves
In this paper we study the propagation of ion-acoustic waves in a collisionless plasma, when different scales of variation are imposed. A modified...