scholarly journals Exact solutions of the cubic Boussinesq and the coupled Higgs system

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 333-342
Author(s):  
Mahmoud Abdelrahman ◽  
Hanan Alkhidhr ◽  
Dumitru Baleanu ◽  
Mustafa Inc
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Test Problems ◽  
Explicit Solutions ◽  
Computational Results ◽  
Special Test ◽  
Elementary Functions ◽  
The Unified Method ◽  
Unified Method

We present explicit exact solutions of some evolution equations including cubic Boussinesq and coupled Higgs system by the unified method. The explicit solutions are expressed in terms of some elementary functions including trigonometric, exponential, and polynomial. The method is applied to a number of special test problems to test the strength of the method and computational results indicate the power and efficiency of the method.

scholarly journals Exact solutions of the cubic Boussinesq and the coupled Higgs system

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 333-342
Author(s):  
Mahmoud Abdelrahman ◽  
Hanan Alkhidhr ◽  
Dumitru Baleanu ◽  
Mustafa Inc
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Test Problems ◽  
Explicit Solutions ◽  
Computational Results ◽  
Special Test ◽  
Elementary Functions ◽  
The Unified Method ◽  
Unified Method

We present explicit exact solutions of some evolution equations including cubic Boussinesq and coupled Higgs system by the unified method. The explicit solutions are expressed in terms of some elementary functions including trigonometric, exponential, and polynomial. The method is applied to a number of special test problems to test the strength of the method and computational results indicate the power and efficiency of the method.

scholarly journals The unified method for abundant soliton solutions of local time fractional nonlinear evolution equations

2021 ◽  
Vol 22 ◽  
pp. 103979
Author(s):  
Nauman Raza ◽  
Muhammad Hamza Rafiq ◽  
Melike Kaplan ◽  
Sunil Kumar ◽  
Yu-Ming Chu
Keyword(s):  
Local Time ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
The Unified Method ◽  
Unified Method

scholarly journals Traveling wave solutions for (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity

2019 ◽  
Vol 8 (1) ◽  
pp. 559-567 ◽  
Author(s):  
M.S. Osman ◽  
Hadi Rezazadeh ◽  
Mostafa Eslami
Keyword(s):  
Applied Sciences ◽  
Power Law ◽  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Mathematical Tool ◽  
Rational Solutions ◽  
Wave Solutions ◽  
The Unified Method ◽  
Soliton Wave Solutions ◽  
Unified Method

Abstract In this work, we consider the (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity. Solitary wave solutions, soliton wave solutions, elliptic wave solutions, and periodic (hyperbolic) wave rational solutions are obtained by means of the unified method. The solutions showed that this method provides us with a powerful mathematical tool for solving nonlinear conformable fractional evolution equations in various fields of applied sciences.

Lie symmetry analysis and dynamical structures of soliton solutions for the (2 + 1)-dimensional modified CBS equation

2020 ◽  
Vol 34 (25) ◽  
pp. 2050221
Author(s):  
S. Kumar ◽  
D. Kumar
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Surface Condition ◽  
Dynamical Behavior ◽  
Lie Symmetry ◽  
Nonlinear Evolution Equations ◽  
Optimal System ◽  
Explicit Solutions ◽  
Nonlinear Odes ◽  
Symmetry Reductions

In this present article, the new [Formula: see text]-dimensional modified Calogero-Bogoyavlenskii-Schiff (mCBS) equation is studied. Using the Lie group of transformation method, all of the vector fields, commutation table, invariant surface condition, Lie symmetry reductions, infinitesimal generators and explicit solutions are constructed. As we all know, an optimal system contains constructively important information about the various types of exact solutions and it also offers clear understandings into the exact solutions and its features. The symmetry reductions of [Formula: see text]-dimensional mCBS equation is derived from an optimal system of one-dimensional subalgebra of the Lie invariance algebra. Then, the mCBS equation can further be reduced into a number of nonlinear ODEs. The generated explicit solutions have different wave structures of solitons and they are analyzed graphically and physically in order to exhibit their dynamical behavior through 3D, 2D-shapes and respective contour plots. All the produced solutions are definitely new and totally different from the earlier study of the Manukure and Zhou (Int. J. Mod. Phys. B 33, (2019)). Some of these solutions are demonstrated by the means of solitary wave profiles like traveling wave, multi-solitons, doubly solitons, parabolic waves and singular soliton. The calculations show that this Lie symmetry method is highly powerful, productive and useful to study analytically other nonlinear evolution equations in acoustics physics, plasma physics, fluid dynamics, mathematical biology, mathematical physics and many other related fields of physical sciences.

scholarly journals A Generalized Kundu-Eckhaus Equation With An Extra-Dispersion: Pulses Configuration

2021 ◽  
Author(s):  
Hamdy. Abdel-Gawad
Keyword(s):  
Exact Solutions ◽  
Optical Fibers ◽  
Phase Modulation ◽  
Raman Effect ◽  
Optical Pulses ◽  
Spectral Content ◽  
Sharp Waves ◽  
The Unified Method ◽  
Unified Method ◽  
Cascade Complex

Abstract Raman effect is due to self-phase modulation (SPM), which is embedded in Kundu-Eckhaus equation KEE. Here, a generalized KEE is suggested by accounting for an extra dispersion. Here, we are concerned with finding the exact solutions of the proposed equation, which is done by using the unified method. In this work, we aim to show that the optical pulses OPs propagation in optical fibers may show a variety of shapes. Waves of multiple geometric shapes are observed. Among these waves, hybrid lumps, soliton, cascade, complex chirped, hybrid w-shaped, rhombus (diamond) waves and soliton modulation, which is induced by SPM. Further, the pulses intensity, frequency, wavelength, polarization, and spectral content are introduced. The results found here are of great interest in experimenting the effects of the induced dispersion on pulses configurations. Further, the colliding dynamics are inspected and as it is observed that no rogue or sharp waves formation holds, so the collision is elastic.

A UNIFIED THEORY OF MEASUREMENT OF ANISOTROPIC RESISTIVITY BASED ON A SINGLE SURFACE OF ONE (FROM THIN TO THICK) FILM

2012 ◽  
Vol 26 (29) ◽  
pp. 1250142
Author(s):  
YUAN HE ◽  
XIANG XIANG ◽  
XIANXI DAI ◽  
WILLIAM E. EVENSON
Keyword(s):  
Thin Films ◽  
Exact Solutions ◽  
Theory Of Measurement ◽  
Simultaneous Equation ◽  
Type I ◽  
Unified Theory ◽  
Type Ii ◽  
Elementary Functions ◽  
Simultaneous Equation Systems ◽  
Unified Method

A unified method and theory for measuring anisotropic resistivity based on a single surface of a film with rapidly converging exact solutions is presented here for solutions appropriate to thin films (Type I solutions) and to thick samples (Type II solutions). Some of the exact solutions of the related simultaneous equation systems can be expressed in terms of elementary functions. The theory proposed here for measuring resistivity of anisotropic crystals is expected to be useful in many applications.

Analytical solutions of the fifth-order time fractional nonlinear evolution equations by the unified method

2021 ◽  
Author(s):  
Abdul Majeed ◽  
Muhammad Naveed Rafiq ◽  
Mohsin Kamran ◽  
Muhammad Abbas ◽  
Mustafa Inc
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Important Goal ◽  
Sense Of Time ◽  
Fifth Order ◽  
The Unified Method ◽  
Unified Method

This key purpose of this study is to investigate soliton solution of the fifth-order Sawada–Kotera and Caudrey–Dodd–Gibbon equations in the sense of time fractional local [Formula: see text]-derivatives. This important goal is achieved by employing the unified method. As a result, a number of dark and rational soliton solutions to the nonlinear model are retrieved. Some of the achieved solutions are illustrated graphically in order to fully understand their physical behavior. The results demonstrate that the presented approach is more effective in solving issues in mathematical physics and other fields.

scholarly journals ON p – q DUALITY AND EXPLICIT SOLUTIONS IN c ≤ 1 2D GRAVITY MODELS

1995 ◽  
Vol 10 (08) ◽  
pp. 1219-1236 ◽  
Author(s):  
S. KHARCHEV ◽  
A. MARSHAKOV
Keyword(s):  
String Theory ◽  
Exact Solutions ◽  
2D Gravity ◽  
Integral Formula ◽  
Integral Representations ◽  
Gravity Models ◽  
Explicit Solutions ◽  
String Equation ◽  
Duality Transformation

We study the role of integral representations in the description of nonperturbative solutions to c ≤ 1 string theory. A generic solution is determined by two functions, W(x) and Q(x), which behave at infinity like xp and xq respectively. The integral formula for arbitrary (p, q) models is derived, which explicitly realizes a duality transformation between (p, q) and (q, p) 2D gravity solutions. We also discuss the exact solutions to the string equation and reduction condition and present several explicit examples.

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