Bright and singular soliton solutions of the conformable time-fractional Klein–Gordon equations with different nonlinearities

2017 ◽  
Vol 28 (3) ◽  
pp. 426-434 ◽  
Author(s):  
Kamyar Hosseini ◽  
Peyman Mayeli ◽  
Reza Ansari
Keyword(s):  
Soliton Solutions ◽  
Klein Gordon ◽  
Singular Soliton

scholarly journals New and More Solitary Wave Solutions for the Klein-Gordon-Schrödinger Model Arising in Nucleon-Meson Interaction

2021 ◽  
Vol 9 ◽  
Author(s):  
Nauman Raza ◽  
Saima Arshed ◽  
Asma Rashid Butt ◽  
Dumitru Baleanu
Keyword(s):  
Soliton Solutions ◽  
Expansion Method ◽  
Dark Soliton ◽  
Art Integration ◽  
Scalar Mesons ◽  
Integration Schemes ◽  
Klein Gordon ◽  
Physical Features ◽  
Existence Criteria ◽  
Singular Soliton

This paper considers methods to extract exact, explicit, and new single soliton solutions related to the nonlinear Klein-Gordon-Schrödinger model that is utilized in the study of neutral scalar mesons associated with conserved scalar nucleons coupled through the Yukawa interaction. Three state of the art integration schemes, namely, the e−Φ(ξ)-expansion method, Kudryashov's method, and the tanh-coth expansion method are employed to extract bright soliton, dark soliton, periodic soliton, combo soliton, kink soliton, and singular soliton solutions. All the constructed solutions satisfy their existence criteria. It is shown that these methods are concise, straightforward, promising, and reliable mathematical tools to untangle the physical features of mathematical physics equations.

scholarly journals Applications of the extended rational sine-cosine and sinh-cosh techniques to some nonlinear complex models arising in mathematical physics

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ayse Nur Akkılıc ◽  
Tukur Abdulkadir Sulaiman ◽  
Hasan Bulut
Keyword(s):  
Soliton Solutions ◽  
Mathematical Physics ◽  
Periodic Wave ◽  
Wave Solutions ◽  
Klein Gordon ◽  
Complex Models ◽  
Physical Features ◽  
Singular Soliton

Abstract This study presents the applications of the extended rational sine-cosine/sinh-cosh schemes to the Klein-Gordon-Zakharov equations and the (2+1)-dimensional Maccari system. Various wave solutions such as singular periodic, periodic wave, topological, topological kink-type, dark and singular soliton solutions are successfully revealed. To display the physical features of the reported solutions, we use some appropriate choice of parameters in plotting the 3D, 2D, and contour graphs of some attained solutions.

Two integrable extensions of the Kadomtsev-Petviashvili equation

Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Kp Equation ◽  
Completely Integrable ◽  
Multiple Soliton Solutions ◽  
Petviashvili Equation ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

AbstractIn this work, two new completely integrable extensions of the Kadomtsev-Petviashvili (eKP) equation are developed. Multiple soliton solutions and multiple singular soliton solutions are derived to demonstrate the compatibility of the extensions of the KP equation.

Multiple Soliton Solutions for a Variety of Coupled Modified Korteweg–de Vries Equations

2011 ◽  
Vol 66 (10-11) ◽  
pp. 625-631
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Mkdv Equation ◽  
Resonance Phenomenon ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Multiple Soliton Solutions ◽  
De Vries ◽  
Coupled Equation ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

We make use of Hirota’s bilinear method with computer symbolic computation to study a variety of coupled modified Korteweg-de Vries (mKdV) equations. Multiple soliton solutions and multiple singular soliton solutions are obtained for each coupled equation. The resonance phenomenon of each coupled mKdV equation is proved not to exist.

BILINEAR FORM AND SOLITON SOLUTIONS FOR THE COUPLED NONLINEAR KLEIN–GORDON EQUATIONS

2012 ◽  
Vol 26 (15) ◽  
pp. 1250057
Author(s):  
HE LI ◽  
XIANG-HUA MENG ◽  
BO TIAN
Keyword(s):  
Field Theory ◽  
Bilinear Form ◽  
Gordon Equation ◽  
Relativistic Quantum ◽  
Soliton Solutions ◽  
Relativistic Quantum Mechanics ◽  
Klein Gordon ◽  
Truncated Painlevé Expansion ◽  
Klein Gordon Equation ◽  
Singular Manifolds

With the coupling of a scalar field, a generalization of the nonlinear Klein–Gordon equation which arises in the relativistic quantum mechanics and field theory, i.e., the coupled nonlinear Klein–Gordon equations, is investigated via the Hirota method. With the truncated Painlevé expansion at the constant level term with two singular manifolds, the coupled nonlinear Klein–Gordon equations are transformed to a bilinear form. Starting from the bilinear form, with symbolic computation, we obtain the N-soliton solutions for the coupled nonlinear Klein–Gordon equations.

Highly dispersive optical soliton perturbation of Kudryashov’s arbitrary form having sextic-power law refractive index

2021 ◽  
Vol 35 (24) ◽  
Author(s):  
Ahmed M. Elsherbeny ◽  
Reda El-Barkouky ◽  
Aly R. Seadawy ◽  
Hamdy M. Ahmed ◽  
Rabab M. I. El-Hassani ◽  
...  
Keyword(s):  
Refractive Index ◽  
Power Law ◽  
Soliton Solutions ◽  
Research Paper ◽  
Optical Soliton ◽  
Integration Scheme ◽  
Arbitrary Form ◽  
Soliton Perturbation ◽  
Singular Soliton ◽  
Simple Integration

In this research paper, a simple integration scheme is executed to secure new dark and singular soliton solutions for the highly dispersive nonlinear Schrödinger’s equation having Kudryashov’s arbitrary form with generalized nonlocal laws and sextic-power law refractive index.

Optical bright, dark and dipole solitons with derivative nonlinearity in the presence of parity-time-symmetric lattices

2020 ◽  
Vol 34 (16) ◽  
pp. 2050174
Author(s):  
Asad Zubair ◽  
Nauman Raza
Keyword(s):  
Nonlinear Medium ◽  
Soliton Solutions ◽  
Optical Solitons ◽  
Arbitrary Power ◽  
Derivative Term ◽  
Linear And Nonlinear ◽  
New Formula ◽  
Singular Soliton ◽  
Engineering Scheme

This paper deals with the study of optical solitons in the presence of new linear and nonlinear parity-time [Formula: see text]-symmetric modulation lattices. The nonlinear medium is a derivative term with arbitrary power. Inverse engineering scheme is utilized to retrieve bright, dark, dipole and singular soliton solutions. These solutions are presented for four new [Formula: see text]-symmetric potentials. The results reveal that optical bright, dark and dipole solitons can exist for those new physical settings.

scholarly journals Topological Soliton Solution and Bifurcation Analysis of the Klein-Gordon-Zakharov Equation in(1+1)-Dimensions with Power Law Nonlinearity

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ming Song ◽  
Bouthina S. Ahmed ◽  
Anjan Biswas
Keyword(s):  
Finite Difference ◽  
Numerical Simulations ◽  
Power Law ◽  
Soliton Solution ◽  
Bifurcation Analysis ◽  
Soliton Solutions ◽  
Phase Portraits ◽  
Zakharov Equation ◽  
Topological Soliton ◽  
Klein Gordon

This paper addresses the Klein-Gordon-Zakharov equation with power law nonlinearity in (1+1)-dimensions. The integrability aspect as well as the bifurcation analysis is studied in this paper. The numerical simulations are also given where the finite difference approach was utilized. There are a few constraint conditions that naturally evolve during the course of derivation of the soliton solutions. These constraint conditions must remain valid in order for the soliton solution to exist. For the bifurcation analysis, the phase portraits are also given.

Optical solitons in nonlinear directional couplers with G′/G-expansion scheme

2015 ◽  
Vol 24 (02) ◽  
pp. 1550017 ◽  
Author(s):  
Mohammad Mirzazadeh ◽  
Mostafa Eslami ◽  
Qin Zhou ◽  
M. F. Mahmood ◽  
Essaid Zerrad ◽  
...  
Keyword(s):  
Power Law ◽  
Soliton Solutions ◽  
Nearest Neighbors ◽  
Optical Solitons ◽  
Nonlinear Media ◽  
Parabolic Law ◽  
Kerr Law ◽  
Singular Soliton ◽  
Optical Couplers ◽  
Expansion Scheme

This paper obtains soliton solutions in optical couplers. The governing equation is solved by the aid of G′/G-expansion scheme. There are four types of nonlinear media that are taken into consideration. These are Kerr law, power law, parabolic law, and dual-power law. There are two kinds optical couplers studied in this paper. They are twin-core couplers and multiple-core couplers, where coupling with nearest neighbors as well as coupling with all neighbors are considered. Dark and singular soliton solutions are retrieved. These soliton solutions come with constraint conditions that must hold for the solitons to exist.

Sign in / Sign up

Export Citation Format

Share Document