On the Travelling Waves for the Generalized Nonlinear Schrödinger Equation
This paper is devoted to the analysis of the travelling waves for a class of generalized nonlinear Schrödinger equations in a cylindric domain. Searching for travelling waves reduces the problem to the multiparameter eigenvalue problems for a class of perturbed p-Laplacians. We study dispersion rel...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/181369 |
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| _version_ | 1849691565666074624 |
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| author | Mahir Hasanov |
| author_facet | Mahir Hasanov |
| author_sort | Mahir Hasanov |
| collection | DOAJ |
| description | This paper is devoted to the analysis of the travelling waves for a
class of generalized nonlinear Schrödinger equations in a cylindric domain. Searching for travelling waves reduces the problem to the multiparameter eigenvalue problems for a class of perturbed p-Laplacians.
We study dispersion relations between the eigenparameters, quantitative analysis of eigenfunctions and discuss some variational principles for eigenvalues of perturbed p-Laplacians. In this paper we analyze the Dirichlet, Neumann, No-flux, Robin and Steklov boundary value problems. Particularly, a “duality principle” between the Robin and the Steklov problems is presented. |
| format | Article |
| id | doaj-art-e212413b48ec4201a4b9b53668c9e850 |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e212413b48ec4201a4b9b53668c9e8502025-08-20T03:20:59ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/181369181369On the Travelling Waves for the Generalized Nonlinear Schrödinger EquationMahir Hasanov0Department of Mathematics, Faculty of Arts and Sciences, Doğuş University, 34722 Istanbul, TurkeyThis paper is devoted to the analysis of the travelling waves for a class of generalized nonlinear Schrödinger equations in a cylindric domain. Searching for travelling waves reduces the problem to the multiparameter eigenvalue problems for a class of perturbed p-Laplacians. We study dispersion relations between the eigenparameters, quantitative analysis of eigenfunctions and discuss some variational principles for eigenvalues of perturbed p-Laplacians. In this paper we analyze the Dirichlet, Neumann, No-flux, Robin and Steklov boundary value problems. Particularly, a “duality principle” between the Robin and the Steklov problems is presented.http://dx.doi.org/10.1155/2011/181369 |
| spellingShingle | Mahir Hasanov On the Travelling Waves for the Generalized Nonlinear Schrödinger Equation Abstract and Applied Analysis |
| title | On the Travelling Waves for the Generalized Nonlinear Schrödinger Equation |
| title_full | On the Travelling Waves for the Generalized Nonlinear Schrödinger Equation |
| title_fullStr | On the Travelling Waves for the Generalized Nonlinear Schrödinger Equation |
| title_full_unstemmed | On the Travelling Waves for the Generalized Nonlinear Schrödinger Equation |
| title_short | On the Travelling Waves for the Generalized Nonlinear Schrödinger Equation |
| title_sort | on the travelling waves for the generalized nonlinear schrodinger equation |
| url | http://dx.doi.org/10.1155/2011/181369 |
| work_keys_str_mv | AT mahirhasanov onthetravellingwavesforthegeneralizednonlinearschrodingerequation |