一类变系数组合KdV方程新的精确解析解<br>New Exact Analytic Solutions to a Coupled KdV Equation with Variable Coefficients

2011 ◽  
Vol 01 (02) ◽  
pp. 163-166
Author(s):  
洪 宝剑
Keyword(s):  
Kdv Equation ◽  
Analytic Solutions ◽  
Variable Coefficients ◽  
Exact Analytic Solutions ◽  
Coupled Kdv Equation

CIRCUIT IMPLEMENTATIONS OF SOLITON SYSTEMS

1999 ◽  
Vol 09 (04) ◽  
pp. 571-590 ◽  
Author(s):  
ANDREW C. SINGER ◽  
ALAN V. OPPENHEIM
Keyword(s):  
Analog Circuits ◽  
Toda Lattice ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Analytic Solutions ◽  
Complex Signal ◽  
Kdv Equations ◽  
Exact Analytic Solutions ◽  
Signal Processors ◽  
Soliton Collisions

Recently, a large class of nonlinear systems which possess soliton solutions has been discovered for which exact analytic solutions can be found. Solitons are eigenfunctions of these systems which satisfy a form of superposition and display rich signal dynamics as they interact. In this paper, we view solitons as signals and consider exploiting these systems as specialized signal processors which are naturally suited to a number of complex signal processing tasks. New circuit models are presented for two soliton systems, the Toda lattice and the discrete-KdV equations. These analog circuits can generate and process soliton signals and can be used as multiplexers and demultiplexers in a number of potential soliton-based wireless communication applications discussed in [Singer et al.]. A hardware implementation of the Toda lattice circuit is presented, along with a detailed analysis of the dynamics of the system in the presence of additive Gaussian noise. This circuit model appears to be the first such circuit sufficiently accurate to demonstrate true overtaking soliton collisions with a small number of nodes. The discrete-KdV equation, which was largely ignored for having no prior electrical or mechanical analog, provides a convenient means for processing discrete-time soliton signals.

Approximate analytic solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled mKdV equation

2010 ◽  
Vol 19 (8) ◽  
pp. 080204 ◽  
Author(s):  
Zhao Guo-Zhong ◽  
Yu Xi-Jun ◽  
Xu Yun ◽  
Zhu Jiang ◽  
Wu Di
Keyword(s):  
Kdv Equation ◽  
Analytic Solutions ◽  
Mkdv Equation ◽  
Coupled Kdv Equation

scholarly journals Approximate Analytic Solutions of Time-Fractional Hirota-Satsuma Coupled KdV Equation and Coupled MKdV Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jincun Liu ◽  
Hong Li
Keyword(s):  
Kdv Equation ◽  
Taylor Series Expansion ◽  
Analytic Solutions ◽  
Mkdv Equation ◽  
Differential Transform Method ◽  
Two Dimensional ◽  
Transform Method ◽  
Coupled Equations ◽  
Differential Transform ◽  
Coupled Kdv Equation

By introducing the fractional derivative in the sense of Caputo and combining the pretreatment technique to deal with long nonlinear items, the generalized two-dimensional differential transform method is proposed for solving the time-fractional Hirota-Satsuma coupled KdV equation and coupled MKdV equation. The presented method is a numerical method based on the generalized Taylor series expansion which constructs an analytical solution in the form of a polynomial. The numerical results show that the generalized two-dimensional differential transform method is very effective for the fractional coupled equations.

POSITONIC SOLUTIONS OF A VARIABLE-COEFFICIENT KdV EQUATION IN FLUID DYNAMICS AND PLASMA PHYSICS

2001 ◽  
Vol 12 (10) ◽  
pp. 1431-1437 ◽  
Author(s):  
YI-TIAN GAO ◽  
BO TIAN
Keyword(s):  
Fluid Dynamics ◽  
Plasma Physics ◽  
Variable Coefficient ◽  
Kdv Equation ◽  
Analytic Solutions ◽  
Exact Analytic Solutions ◽  
De Vries

Positons are a new concept in nonlinear sciences. In this paper, we report some positonic, exact analytic solutions for a variable-coefficient Korteweg-de Vries (KdV) equation arising from fluid dynamics and plasma physics.

Lie symmetry analysis of the deformed KdV equation

2017 ◽  
Vol 31 (30) ◽  
pp. 1750275 ◽  
Author(s):  
Yehui Huang ◽  
Wei Li ◽  
Guo Wang ◽  
Xuelin Yong
Keyword(s):  
Kdv Equation ◽  
Classical Equation ◽  
Analytic Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
System Method ◽  
Exact Analytic Solutions ◽  
Similarity Reductions

The deformed KdV equation is a generalization of the classical equation that can describe the motion of the interaction between different solitary waves. In this paper, the Lie symmetry analysis is performed on the deformed KdV equation. The similarity reductions and exact solutions are obtained based on the optimal system method. The exact analytic solutions are considered by using the power series method. The conservation laws for the deformed KdV equation are presented. Finally, the analytic solutions are given and their dynamics are studied.

CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

Analytic Solutions to Forced KdV Equation

2009 ◽  
Vol 52 (2) ◽  
pp. 279-283 ◽  
Author(s):  
Zhao Jun-Xiao ◽  
Guo Bo-Ling
Keyword(s):  
Kdv Equation ◽  
Analytic Solutions

scholarly journals Exact analytical solutions of continuously graded models of flat lenses based on transformation optics

2017 ◽  
Vol 30 (4) ◽  
pp. 639-646 ◽  
Author(s):  
Mariana Dalarsson ◽  
Raj Mittra
Keyword(s):  
Magnetic Fields ◽  
Longitudinal Direction ◽  
Middle Layer ◽  
Analytic Solutions ◽  
Transformation Optics ◽  
Confluent Hypergeometric Functions ◽  
Graded Index ◽  
Exact Analytic Solutions ◽  
Electric And Magnetic Fields ◽  
Physical Insight

We present a study of exact analytic solutions for electric and magnetic fields in continuously graded flat lenses designed utilizing transformation optics. The lenses typically consist of a number of layers of graded index dielectrics in both the radial and longitudinal directions, where the central layer in the longitudinal direction primarily contributes to a bulk of the phase transformation, while other layers act as matching layers and reduce the reflections at the interfaces of the middle layer. Such lenses can be modeled as compact composites with continuous permittivity (and if needed) permeability functions which asymptotically approach unity at the boundaries of the composite cylinder. We illustrate the proposed procedures by obtaining the exact analytic solutions for the electric and magnetic fields for one simple special class of composite designs with radially graded parameters. To this purpose we utilize the equivalence between the Helmholtz equation of our graded flat lens and the quantum-mechanical radial Schr?dinger equation with Coulomb potential, furnishing the results in the form of Kummer confluent hypergeometric functions. Our approach allows for a better physical insight into the operation of our transformation optics-based graded lenses and opens a path toward novel designs and approaches.

scholarly journals New Soliton Solutions for the Higher-Dimensional Non-Local Ito Equation

2021 ◽  
Vol 10 (1) ◽  
pp. 374-384
Author(s):  
Mustafa Inc ◽  
E. A. Az-Zo’bi ◽  
Adil Jhangeer ◽  
Hadi Rezazadeh ◽  
Muhammad Nasir Ali ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Solution Process ◽  
Soliton Solutions ◽  
Analytic Solutions ◽  
Bright Solitons ◽  
Exact Analytic Solutions ◽  
Higher Dimensional ◽  
Non Local ◽  
Free Parameters ◽  
Ito Equation

Abstract In this article, (2+1)-dimensional Ito equation that models waves motion on shallow water surfaces is analyzed for exact analytic solutions. Two reliable techniques involving the simplest equation and modified simplest equation algorithms are utilized to find exact solutions of the considered equation involving bright solitons, singular periodic solitons, and singular bright solitons. These solutions are also described graphically while taking suitable values of free parameters. The applied algorithms are effective and convenient in handling the solution process for Ito equation that appears in many phenomena.

Sign in / Sign up

Export Citation Format

Share Document