The solitary wave solution of the two-dimensional regularized long-wave equation in fluids and plasmas

Computer Physics Communications

Volumn 182, Issue 12, 2011, Pages 2540-2549

  Dehghan, Mehdi ^a   Salehi, Rezvan ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Analog equation method; Boundary knot method; Boundary type meshless methods; Radial basis functions; Regularized long wave equation; Solitary waves

Indexed keywords

FINITE DIFFERENCE METHOD; FUNCTIONS; HEAT CONDUCTION; IMAGE SEGMENTATION; MECHANICAL WAVES; NONLINEAR EQUATIONS; RADIAL BASIS FUNCTION NETWORKS; SOLITONS; WAVE EQUATIONS;

ANALOG EQUATION METHODS; BOUNDARY KNOT METHOD; MESH-LESS METHODS; RADIAL BASIS FUNCTIONS; REGULARIZED LONG WAVE EQUATION;

NUMERICAL METHODS;

EID: 80052323256     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2011.07.018     Document Type: Article

References (54)

1. T.B. Benjamin, J.L. Bona, and J.J. Mahony Model equations for long waves in non-linear dispersive systems Philos. Trans. R. Soc. Lond. Ser. A 272 1972 47 78
2. W. Chen, and M. Tanaka New insights in boundary-only and domain-type RBF methods Int. J. Nonlinear Sci. Numer. Simul. 1 2000 145 152 (Pubitemid 33220663)
3. W. Chen, and M. Tanaka A meshfree, integration-free, and boundary-only RBF technique Comput. Math. Appl. 43 2002 379 391 (Pubitemid 34104975)
4. W. Chen, L.J. Shen, Z.J. Shen, and G.W. Yuan Boundary knot method for Poisson equations Engrg. Anal. Bound. Elem. 29 2005 756 760 (Pubitemid 41013886)
5. W. Chen Symmetric boundary knot method Engrg. Anal. Bound. Elem. 26 2002 489 494 (Pubitemid 34498236)
6. I. Dag Least squares quadratic B-spline finite element method for the regularized long wave equation Comput. Methods Mech. Engng. 182 2000 205 215 (Pubitemid 30170556)
7. I. Dag, B. Saka, and D. Irk Galerkin method for the numerical solution of the RLW equation using quintic B-splines J. Comput. Appl. Math. 190 2006 532 547 (Pubitemid 43189968)
8. M. Dehghan Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices Math. Comput. Simulation 71 2006 16 30 (Pubitemid 43243672)
9. M. Dehghan On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation Numer. Methods Partial Differential Equations 21 2005 24 40 (Pubitemid 40030408)
10. M. Dehghan A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications Numer. Methods Partial Differential Equations 22 2006 220 257
11. M. Dehghan The one-dimensional heat equation subject to a boundary integral specification Chaos Solitons Fractals 32 2007 661 675 (Pubitemid 44537757)
12. M. Dehghan, and A. Shokri A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions Math. Comput. Simulation 79 2008 700 715
13. M. Dehghan, H. Hosseinzadeh, Calculation of 2D singular and near singular integrals of boundary element method based on the complex space C, Applied Mathematical Modelling (2011), in press, doi:10.1016/j.apm.2011.07.036.
14. K. Djidjeli, W.G. Price, E.H. Twizell, and Q. Cao A linearized implicit pseudo-spectral method for some model equations-the regularized long wave equations Commun. Numer. Meth. Engng. 19 2003 847 863 (Pubitemid 37497117)
15. J.C. Eilbeck, and G.R. McGuire Numerical study of RLW equation I: Numerical methods J. Comput. Phys. 19 1975 43 57
16. J.C. Eilbeck, and G.R. McGuire Numerical study of the regularized long-wave equation: II-Interaction of solitary waves J. Comput. Phys. 23 1977 63 73
17. B.Y. Guo, and W.M. Cao The Fourier pseudospectral method with a restrain operator for the RLW equation J. Comput. Phys. 74 1988 110 126
18. J. Goldstein, A. Kajikiya, and S. Oharu On some nonlinear dispersive equations in several space variables Differential Integral Equations 3 1990 617 632
19. M.A. Helal Soliton solution of some nonlinear partial differential equations and its applications in fluid mechanics Chaos Solitons Fractals 13 2002 1917 1929 (Pubitemid 34036226)
20. W. Horton, and A. Hasegawa Quasi-two-dimensional dynamics of plasmas and fluids Chaos 4 1994 227 251
21. Y.C. Hon, and W. Chen Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry Int. J. Numer. Meth. Engrg. 56 2003 1931 1948 (Pubitemid 36405756)
22. Z. Huang On Cauchy problems for the RLW equation in two space dimensions Appl. Math. Mech. 23 2002 159 164
23. B. Jin, and Y. Zheng Boundary knot method for the Cauchy problem associated with the inhomogeneous Helmholtz equation Engrg. Anal. Bound. Elem. 29 2005 925 935 (Pubitemid 41455091)
24. B. Jin, and W. Chen Boundary knot method based on geodesic distance for anisotropic problems J. Comput. Phys. 215 2006 614 629 (Pubitemid 43623598)
25. S.P. Hu, C.M. Fan, and D.L. Young The meshless analog equation method for solving heat transfer to molten polymer flow in tubes Int. J. Heat Mass Transfer 53 2010 2240 2247
26. J.T. Katsikadelis The analog equation method-A powerful BEM-based solution technique for solving linear and nonlinear engineering problems C.A. Brebbia, Boundary Element Method XVI 1994 CLM Publications Southampton 167
27. J.T. Katsikadelis, and M.S. Nerantzaki The boundary element method for nonlinear problems Engrg. Anal. Bound. Elem. 23 1999 365 373
28. J.T. Katsikadelis, and G.C. Tsiatas Nonlinear dynamic analysis of heterogeneous orthotropic membranes by the analog equation method Engrg. Anal. Bound. Elem. 27 2003 115 124
29. J.T. Katsikadelis The 2D elastostatic problem in inhomogeneous anisotropic bodies by the meshless analog equation method (MAEM) Engrg. Anal. Bound. Elem. 32 2008 997 1005
30. J.T. Katsikadelis The analog equation method, A boundary-only integral equation method for nonlinear static and dynamic problems in general bodies Int. J. Theor. Appl. Mech. 27 2002 13 38
31. J.T. Katsikadelis Numerical solution of multi-term fractional differential equations ZAMM 89 2009 593 608
32. J.T. Katsikadelis, and M.S. Nerantzaki A Boundary element solution to the soap bubble problem Comput. Mech. 27 2001 154 159 (Pubitemid 32325751)
33. J.T. Katsikadelis The meshless analog equation method: I. Solution of elliptic partial differential equations Arch. Appl. Mech. 79 2009 557 578
34. J.T. Katsikadelis The fractional wave-diffusion equation in bounded inhomogeneous anisotropic media. An AEM solution G.D. Manolis, D. Polyzos, Recent Advances in Boundary Element Methods: A Volume to Honour Professor Dimitri Beskos 2009 Springer Science Dordrecht, Netherlands 255 276
35. T. Kawahara, K. Araki, and S. Toh Interactions of two-dimensionally localized pulses of the regularized-long-wave equation Phys. D 59 1992 79 89
36. A.K. Khalifa, K.R. Raslan, and H.M. Alzubaidi A finite difference scheme for the MRLW and solitary wave interactions Appl. Math. Comput. 189 2007 346 354 (Pubitemid 46738586)
37. J. Lin, Z. Xie, and J. Zhou High-order compact difference scheme for the regularized long wave equation Comm. Numer. Methods Engrg. 23 2007 135 156 (Pubitemid 46210534)
38. D. Mirzaei, and M. Dehghan A meshless based method for solution of integral equations Appl. Numer. Math. 60 2010 245 262
39. D. Mirzaei, and M. Dehghan MLPG method for transient heat conduction problem with MLS as trial approximation in both time and space domains, Computer Modeling in Engineering and Sciences CMES 72 2011 185 210
40. M.G. Prahovic, R.D. Hazeltine, and P.J. Morrison Exact solutions for a system of nonlinear plasma fluid equations Phys. Fluids B 4 1992 831 840
41. D.H. Peregrine Calculations of the development of an undular bore J. Fluid Mech. 25 1966 321 330
42. B. Saka, and I. Dag A numerical solution of the RLW equation by Galerkin method using quartic B-splines Comm. Numer. Methods Engrg. 24 2008 1339 1361
43. A. Shokri, and M. Dehghan A meshless method using the radial basis functions for numerical solution of the regularized long wave equation Numer. Methods Partial Differential Equations 26 2010 807 825
44. Y. Shang, and P. Niu Explicit exact solutions for the RLW equation and the SRLW equation in two space dimensions Math. Appl. 11 1988 1 5
45. X.N. Su, W. Horton, and P.J. Morrison Drift wave vortices in inhomogeneous plasmas Phys. Fluids B 3 1991 921 930
46. M. Tatari, and M. Dehghan On the solution of the non-local parabolic partial differential equations via radial basis functions Appl. Math. Model. 33 2009 1729 1738
47. B. Tian, W. Li, and Y.T. Gao On the two-dimensional regularized long-wave equation in fluids and plasmas Acta Mech. 160 2003 235 239
48. K. Wiklund, Non-linear wave interaction in a Hamiltonian family of Hasegawa-Mima related equation, in: 27th EPS Conference on Contr. Fusion and Plasma Phys., Budapest 24B, 2000, pp. 1280-1283.
49. Q. Wang, and M. Huang The numerical simulation of solitary wave on regular long wave equation Acta Sci. Nat. Univ. Jilinensis 3 1997 1 13
50. F. Wang, W. Chen, and Xi. Jiang Investigation of regularized techniques for boundary knot method Int. J. Numer. Meth. Biomed. Engn. 26 2010 1868 1877
51. A.M. Wazwaz Partial Differential Equations and Solitary Waves Theory 2009 Springer New York
52. A.M. Wazwaz Analytic study on nonlinear variants of the RLW and the phi-four equations Commun. Nonlinear Sci. Numer. Simul. 12 2007 314 327
53. H. Zheng-hong On Cauchy problems for the RLW equation in two space dimensional Appl. Math. Mech. 23 2002 169 177
54. L. Zhang A finite difference scheme for generalized regularized long-wave equation Appl. Math. Comput. 168 2005 962 972 (Pubitemid 41405654)