Analytic method for solitary solutions of some partial differential equations

Uğurlu, Yavuz; Kaya, Doǧan

doi:10.1016/j.physleta.2007.05.057

Cited by 25 publications

(12 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The STO equation appears in many scientific applications such as in plasma physics, quantum field theory, nonlinear optics, dispersive wave phenomena and relativistic physics. 2,5,6 Also it arises as an evolution equation that possesses finitely many symmetries. 8 A number of theoretical issues associated to the STO equation have received substantial attention.…”

Section: Introductionmentioning

confidence: 99%

The Petrov–Galerkin finite element method for the numerical solution of time-fractional Sharma–Tasso–Olver equation

Gupta

Ray

2019

Int. J. Model. Simul. Sci. Comput.

View full text Add to dashboard Cite

In this paper, time-fractional Sharma–Tasso–Olver (STO) equation has been solved numerically through the Petrov–Galerkin approach utilizing a quintic B-spline function as the test function and a linear hat function as the trial function. The Petrov–Galerkin technique is effectively implemented to the fractional STO equation for acquiring the approximate solution numerically. The numerical outcomes are observed in adequate compatibility with those obtained from variational iteration method (VIM) and exact solutions. For fractional order, the numerical outcomes of fractional Sharma–Tasso–Olver equations are also compared with those obtained by variational iteration method (VIM) in Song et al. [Song L., Wang Q., Zhang H., Rational approximation solution of the fractional Sharma–Tasso–Olver equation, J. Comput. Appl. Math. 224:210–218, 2009]. Numerical experiments exhibit the accuracy and efficiency of the approach in order to solve nonlinear fractional STO equation.

show abstract

Section: Introductionmentioning

confidence: 99%

The Petrov–Galerkin finite element method for the numerical solution of time-fractional Sharma–Tasso–Olver equation

Gupta

Ray

2019

Int. J. Model. Simul. Sci. Comput.

View full text Add to dashboard Cite

show abstract

“…Moreover, the multiple solitons, exact traveling solutions, kinks solutions, non-traveling wave solutions of the STO equation were obtained with different approaches applied on it. [21][22][23][24][25][26][27][28][29][30][31][32] This paper is concerned with the following equation, called the complex Sharma-Tasso-Olver (CSTO) equation derived by Fan,25 …”

Section: Introductionmentioning

confidence: 99%

Algebro-geometric solutions for the complex Sharma-Tasso-Olver hierarchy

Yue

Xia

2014

Journal of Mathematical Physics

View full text Add to dashboard Cite

This paper is dedicated to provide theta function representation of algebro-geometric solutions and related crucial quantities for the complex Sharma-Tasso-Olver (CSTO) hierarchy. Our main tools include the polynomial recursive formalism to derive the CSTO hierarchy, the hyper-elliptic curve with finite number of genus, the Baker-Akhiezer functions, the meromorphic function, the Dubrovin-type equations for auxiliary divisors, and the associated trace formulas. By use of these tools, the explicit representations of the Baker-Ahhiezer functions, the meromorphic function, and the algebro-geometric solutions are obtained for the entire CSTO hierarchy. C 2014 AIP Publishing LLC. [http://dx.

show abstract

“…The STO equation (1) appears in many scientific applications such as in quantum field theory, relativistic physics, dispersive wave phenomena, plasma physics, nonlinear optics, and applied and physical sciences [1][2][3] . Many authors have studied the STO equation (1) in recent years because of its applications in several areas of interest (see Refs. 4-6 and the references therein).…”

Section: Introductionmentioning

confidence: 99%

On the solutions and conservation laws for the Sharma-Tasso-Olver equation

Johnpillai¹,

Khalique²

2014

ScienceAsia

View full text Add to dashboard Cite

ABSTRACT:We study the Sharma-Tasso-Olver equation from the Lie symmetry point of view. We derive the Lie point symmetry generators of the equation and classify them to obtain the optimal system of one-dimensional subalgebras of the Lie symmetry algebra of the equation. These subalgebras are then used to construct symmetry reductions for the equation. We obtain the general solution of the nonlinear second-order ordinary differential equation which results from the symmetry reduction for the travelling wave group-invariant solutions of the equation by transforming it into a linear third-order ordinary differential equation through a Riccati transformation. Then we show that one can easily obtain the travelling wave exact group-invariant solutions for the underlying equation by using the general solution of the linearized third-order ordinary differential equation and the Riccati transformation. We also construct conservation laws for the underlying equation by making use of the multiplier method.

show abstract

Analytic method for solitary solutions of some partial differential equations

Cited by 25 publications

References 19 publications

The Petrov–Galerkin finite element method for the numerical solution of time-fractional Sharma–Tasso–Olver equation

The Petrov–Galerkin finite element method for the numerical solution of time-fractional Sharma–Tasso–Olver equation

Algebro-geometric solutions for the complex Sharma-Tasso-Olver hierarchy

On the solutions and conservation laws for the Sharma-Tasso-Olver equation

Contact Info

Product

Resources

About