SOLITARY WAVES OF TWO-DIMENSIONAL MODIFIED KAWAHARA EQUATION


Cite this article as:

Katson V. М. SOLITARY WAVES OF TWO-DIMENSIONAL MODIFIED KAWAHARA EQUATION. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 6, pp. 76-85. DOI: https://doi.org/10.18500/0869-6632-2008-16-6-76-85


Equations of this type describe a number of real-life processes like wave motion under ice mantle or propagation of waves of longitudinal deformation in thin cylinder shell. Using «Simplest Equation Method» exact solitary-wave solutions of the two-dimensional Kawahara Equation were obtained. On the basis of implicit pseudospectral method the numerical investigation is carried out. Regimes of two-dimensional deformation waves with classic solitary behavior were discovered.

Key words: 
-
DOI: 
10.18500/0869-6632-2008-16-6-76-85
Literature

1. Kawahara T. Oscillatory solitary waves in dispersive media // J. Phys. Soc. Japan. 1972. Vol. 33. No 1. P. 260.

2. Марченко А.В. О длинных волнах в мелкой жидкости под ледяным покровом // ПММ. 1988. Т. 52, вып. 2. С. 230.

3. Горшков К.А., Островский Л.А., Папко В.В. Взаимодействия и связанные состояния солитонов как классических частиц // ЖЭТФ. 1976. Т. 71, No 2. C. 585.

4. Землянухин А.И. , Могилевич Л.И. Нелинейные волны в цилиндрических оболочках: солитоны, симметрии, эволюция. Саратов: Сарат. гос. техн. ун-т, 1999. 132 с.

5. Weiss J., Tabor M., Carnevale G. The Painleve property for partial differential equation // J. Math. Phys. 1983. Vol. 24, No 3. P. 522.

6. Кудряшов Н.А. Точные решения нелинейных волновых уравнений, встречающихся в механике // ПММ. 1990. Т. 54, вып. 3. С. 450.

7. Кудряшов Н.А. Simplest equation method to look for exact solutions of nonlinear differential equations // Chaos, Solitons and Fractals. 2005. Vol. 24. P. 1217.

8. Землянухин А.И., Катсон В.М. Теория и практика спектральных методов решения уравнений с частными производными: учебное пособие Волгоград: Волг-ГАСУ, 2007. 56 с.

9. Numerical recipes in C. The art of scientific computing. / Eds. W.H. Press, S.L. Teukolsky, W.T. Vettenberg, B.P. Flannery. Second edition. Cambridge : Cambridge University Press, 1992. 680 p.

Heading: 
Status: 
одобрено к публикации
Short Text (PDF): 
Full Text (PDF): 

BibTeX

@article{Катсон -IzvVUZ_AND-16-6-76,
author = {V. М. Katson},
title = {SOLITARY WAVES OF TWO-DIMENSIONAL MODIFIED KAWAHARA EQUATION},
year = {2008},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {16},number = {6},
url = {https://old-andjournal.sgu.ru/en/articles/solitary-waves-of-two-dimensional-modified-kawahara-equation},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2008-16-6-76-85},pages = {76--85},issn = {0869-6632},
keywords = {-},
abstract = {Equations of this type describe a number of real-life processes like wave motion under ice mantle or propagation of waves of longitudinal deformation in thin cylinder shell. Using «Simplest Equation Method» exact solitary-wave solutions of the two-dimensional Kawahara Equation were obtained. On the basis of implicit pseudospectral method the numerical investigation is carried out. Regimes of two-dimensional deformation waves with classic solitary behavior were discovered. }}