scholarly journals On the exact solutions to some system of complex nonlinear models

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Tukur Abdulkadir Sulaiman ◽  
Hasan Bulut ◽  
Haci Mehmet Baskonus
Keyword(s):  
Gravity Waves ◽  
Gordon Equation ◽  
Nonlinear Models ◽  
Expansion Method ◽  
Multiple Scale ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Complex Models ◽  
Nonlinear Surface ◽  
Singular Soliton

AbstractIn this manuscript, the application of the extended sinh-Gordon equation expansion method to the Davey-Stewartson equation and the (2+1)-dimensional nonlinear complex coupled Maccari system is presented. The Davey-Stewartson equation arises as a result of multiple-scale analysis of modulated nonlinear surface gravity waves propagating over a horizontal seabed and the (2+1)-dimensional nonlinear complex coupled Maccari equation describes the motion of the isolated waves, localized in a small part of space, in many fields such as hydrodynamic, plasma physics, nonlinear optics. We successfully construct some soliton, singular soliton and singular periodic wave solutions to these two nonlinear complex models. The 2D, 3D and contour graphs to some of the obtained solutions are presented.

scholarly journals An Extension of the Double G ′ / G ,   1 / G -Expansion Method for Conformable Fractional Differential Equations

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Altaf A. Al-Shawba ◽  
Farah A. Abdullah ◽  
Amirah Azmi ◽  
M. Ali Akbar
Keyword(s):  
Wave Motion ◽  
Nonlinear Models ◽  
Expansion Method ◽  
Periodic Wave ◽  
Relativistic Wave ◽  
Conformable Derivative ◽  
Fractional Systems ◽  
Periodic Wave Solutions ◽  
Engineering Problems ◽  
Fractional Differential

The phenomena, molecular path in a liquid or a gas, fluctuating price stoke, fission and fusion, quantum field theory, relativistic wave motion, etc., are modeled through the nonlinear time fractional clannish random Walker’s parabolic (CRWP) equation, nonlinear time fractional SharmaTassoOlver (STO) equation, and the nonlinear space-time fractional KleinGordon equation. The fractional derivative is described in the sense of conformable derivative. From there, the G ′ / G ,   1 / G -expansion method is found to be ensuing, effective, and capable to provide functional solutions to nonlinear models concerning physical and engineering problems. In this study, an extension of the G ′ / G ,   1 / G -expansion method has been introduced. This enhancement establishes broad-ranging and adequate fresh solutions. In addition, some existing solutions attainable in the literature also confirm the validity of the suggested extension. We believe that the extension might be added to the literature as a reliable and efficient technique to examine a wide variety of nonlinear fractional systems with parameters including solitary and periodic wave solutions to nonlinear FDEs.

M-fractional solitons and periodic wave solutions to the Hirota–Maccari system

2019 ◽  
Vol 33 (05) ◽  
pp. 1950052 ◽  
Author(s):  
Tukur Abdulkadir Sulaiman ◽  
Gulnur Yel ◽  
Hasan Bulut
Keyword(s):  
Fractional Derivative ◽  
Gordon Equation ◽  
Expansion Method ◽  
Periodic Wave ◽  
3 Dimensional ◽  
Periodic Wave Solutions ◽  
Wave Solutions

In this study, we construct several wave solutions to the nonlinear fractional Hirota–Maccari equation with a truncated M-fractional derivative via the extended sinh-Gordon equation expansion method. The constraint conditions that guarantee the existence of valid solutions are stated. We use suitable values of parameters in plotting the 2- and 3-dimensional graphs of the reported solutions.

ANALYTICAL STUDY ON NONLINEAR DIFFERENTIAL–DIFFERENCE EQUATIONS VIA A NEW METHOD

2010 ◽  
Vol 24 (08) ◽  
pp. 761-773
Author(s):  
HONG ZHAO
Keyword(s):  
Difference Equations ◽  
Elliptic Function ◽  
Analytical Study ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Jacobian Elliptic Function ◽  
Jacobian Elliptic Functions ◽  
Periodic Wave Solutions ◽  
Trigonometric Function Solutions

Based on the computerized symbolic computation, a new rational expansion method using the Jacobian elliptic function was presented by means of a new general ansätz and the relations among the Jacobian elliptic functions. The results demonstrated an effective direction in terms of a uniformed construction of the new exact periodic solutions for nonlinear differential–difference equations, where two representative examples were chosen to illustrate the applications. Various periodic wave solutions, including Jacobian elliptic sine function, Jacobian elliptic cosine function and the third elliptic function solutions, were obtained. Furthermore, the solitonic solutions and trigonometric function solutions were also obtained within the limit conditions in this paper.

Nonlocal Symmetry and Consistent Tanh Expansion Method for the Coupled Integrable Dispersionless Equation

2016 ◽  
Vol 71 (3) ◽  
pp. 235-240 ◽  
Author(s):  
Hengchun Hu ◽  
Xiao Hu ◽  
Bao-Feng Feng
Keyword(s):  
Soliton Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Cnoidal Wave ◽  
Nonlocal Symmetry ◽  
Nonlocal Symmetries ◽  
Periodic Wave Solutions ◽  
Wave Solutions

AbstractNonlocal symmetries are obtained for the coupled integrable dispersionless (CID) equation. The CID equation is proved to be consistent, tanh-expansion solvable. New, exact interaction excitations such as soliton–cnoidal wave solutions, soliton–periodic wave solutions, and multiple resonant soliton solutions are discussed analytically and shown graphically.

scholarly journals New Exponential and Complex Traveling Wave Solutions to the Konopelchenko-Dubrovsky Model

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Faruk Dusunceli
Keyword(s):  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Nonlinear Ordinary Differential Equation ◽  
Wave Transformation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Parameter Values ◽  
Singular Soliton

The Konopelchenko-Dubrovsky (KD) system is presented by the application of the improved Bernoulli subequation function method (IBSEFM). First, The KD system being Nonlinear partial differential equations system is transformed into nonlinear ordinary differential equation by using a wave transformation. Last, the resulting equation is successfully explored for new explicit exact solutions including singular soliton, kink, and periodic wave solutions. All the obtained solutions in this study satisfy the Konopelchenko-Dubrovsky model. Under suitable choice of the parameter values, interesting two- and three-dimensional graphs of all the obtained solutions are plotted.

RIEMANN THETA FUNCTIONS SOLUTIONS WITH RATIONAL CHARACTERISTICS FOR (2+1)-DIMENSIONAL SINH-GORDON EQUATION

2010 ◽  
Vol 24 (06) ◽  
pp. 575-584
Author(s):  
YANG FENG ◽  
HONG-QING ZHANG
Keyword(s):  
Gordon Equation ◽  
Theta Functions ◽  
Periodic Wave ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Wave Numbers ◽  
Riemann Theta Functions ◽  
The Waves ◽  
Hirota Bilinear

In this letter, we use the Riemann theta functions with rational characteristics and the Hirota bilinear method to construct quasi-periodic wave solutions for (2+1)-dimensional sinh-Gordon equation. This method not only conveniently obtains quasi-periodic solutions of nonlinear equations, but also directly gets the explicit expressions of frequencies, wave numbers, phase and amplitudes for the waves.

Modulation instability analysis and optical solitons of the generalized model for description of propagation pulses in optical fiber with four non-linear terms

2020 ◽  
pp. 2150112
Author(s):  
S. U. Rehman ◽  
Aly R. Seadawy ◽  
M. Younis ◽  
S. T. R. Rizvi ◽  
T. A. Sulaiman ◽  
...  
Keyword(s):  
Optical Fibers ◽  
Modulation Instability ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Arbitrary Power ◽  
Non Linear ◽  
Complex Phenomena ◽  
Singular Soliton

In this article, we investigate the optical soiltons and other solutions to Kudryashov’s equation (KE) that describe the propagation of pulses in optical fibers with four non-linear terms. Non-linear Schrodinger equation with a non-linearity depending on an arbitrary power is the base of this equation. Different kinds of solutions like optical dark, bright, singular soliton solutions, hyperbolic, rational, trigonometric function, as well as Jacobi elliptic function (JEF) solutions are obtained. The strategy that is used to extract the dynamics of soliton is known as [Formula: see text]-model expansion method. Singular periodic wave solutions are recovered and the constraint conditions, which provide the guarantee to the soliton solutions are also reported. Moreover, modulation instability (MI) analysis of the governing equation is also discussed. By selecting the appropriate choices of the parameters, 3D, 2D, and contour graphs and gain spectrum for the MI analysis are sketched. The obtained outcomes show that the applied method is concise, direct, elementary, and can be imposed in more complex phenomena with the assistant of symbolic computations.

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