On general form of the Tanh method and its application to nonlinear partial differential equations

Download

10.3934naco.2016007.pdf

Date

2016-6

Author

Hamidoğlu, Ali

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

204
views

134
downloads

The tanh method is used to compute travelling waves solutions of one-dimensional nonlinear wave and evolution equations. The technique is based on seeking travelling wave solutions in the form of a finite series in tanh. In this article, we introduce a new general form of tanh transformation and solve well-known nonlinear partial differential equations in which tanh method becomes weaker in the sense of obtaining general form of solutions.

Subject Keywords

Tanh method, Nonlinear partial differential equations, Exact solutions, Nonlinear travelling waves

URI

https://hdl.handle.net/11511/52275

Journal

Numerical Algebra, Control and Optimization

DOI

https://doi.org/10.3934/naco.2016007

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

On General Form of Tanh Method and Its Application to Medical Problems Ali, Hamidoglu (2016-09-02) The tanh method is used to compute travelling waves solutions of one-dimensional non-linear wave and evolution equations. The technique is based on seeking travelling wave solutions in the form of a finite series in tanh. However, the mentioned method is not always efficient method to solve some types of one dimensional non-linear partial differential equations in more general sense. In this article, we construct new general transformation of tanh function which is more effective in the sense of getting gen...
On the solution of nonlinear algebraic equations following periodic forced response analysis of nonlinear structures using different nonlinear solvers Kizilay, H. Sefa; Ciğeroğlu, Ender (2021-01-01) In periodic forced response analysis of nonlinear structures, most of the time analytical solutions cannot be obtained due to the complex behavior of the nonlinearity and/or due to the number of nonlinear equations to be solved. Therefore, numerical methods are widely used. For periodic forced response analysis of nonlinear systems, generally Harmonic Balance Method (HBM) or Describing Function Method (DFM), which transform the nonlinear differential equations into a set of nonlinear algebraic equations, ar...
Analytical solutions of shallow-water wave equations Aydın, Baran; Kanoğlu, Utku; Department of Engineering Sciences (2011) Analytical solutions for the linear and nonlinear shallow-water wave equations are developed for evolution and runup of tsunamis –long waves– over one- and two-dimensional bathymetries. In one-dimensional case, the nonlinear equations are solved for a plane beach using the hodograph transformation with eigenfunction expansion or integral transform methods under different initial conditions, i.e., earthquake-generated waves, wind set-down relaxation, and landslide-generated waves. In two-dimensional case, th...
EXACT SPIN AND PSEUDO-SPIN SYMMETRIC SOLUTIONS OF THE DIRAC-KRATZER PROBLEM WITH A TENSOR POTENTIAL VIA LAPLACE TRANSFORM APPROACH Arda, Altug; Sever, Ramazan (2012-09-28) Exact bound state solutions of the Dirac equation for the Kratzer potential in the presence of a tensor potential are studied by using the Laplace transform approach for the cases of spin- and pseudo-spin symmetry. The energy spectrum is obtained in the closed form for the relativistic as well as non-relativistic cases including the Coulomb potential. It is seen that our analytical results are in agreement with the ones given in the literature. The numerical results are also given in a table for different p...
On the consistency of the solutions of the space fractional Schroumldinger equation (vol 53, 042105, 2012) Bayin, Selcuk S. (2012-08-01) Recently we have reanalyzed the consistency of the solutions of the space fractional Schroumldinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are consistent. In this comment, for clarity, we present additional information about the critical integrals and describe how their analytic continuation is accomplished.

Citation Formats

A. Hamidoğlu, “On general form of the Tanh method and its application to nonlinear partial differential equations,” Numerical Algebra, Control and Optimization, pp. 175–181, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52275.