New soliton solutions of the system of equations for the ion sound and Langmuir waves
This study is based on new soliton solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to highfrequency field and for the Langmuir wave. The generalized Kudryashov method (GKM), which is one of the analytical methods, has been tackled for finding exact solutions of the system of equations for the ion sound wave and the Langmuir wave. By using this method, dark soliton solutions of this system of equations have been obtained. Also, by using Mathematica Release 9, some graphical simulations were designed to see the behavior of these solutions
[1] Cher, Y., Czubak, M., and Sulem, C., Blowing Up Solutions to the Zakharov System for LangmuirWaves, Laser Filamentation, Springer International Publishing, 77-95 (2016).
[2] Eslami, M., Trial solution technique to chiral nonlinear Schrodinger’s equation in (1+2)- dimensions, Nonlinear Dynamics, 85, 813-816 (2016).
[3] Hammouch, Z., and Mekkaoui, T., Traveling-wave solutionsof the generalized Zakharov equation with time-space fractional derivatives, Mathematics in Engineering, Science and Aerospace, 5(4), 489-498 (2014).
[4] Hammouch, Z., and Mekkaoui, T., Travellingwavesolutions for some fractional partial differential equation by means ofgeneralized trigonometry functions, International Journal of Applied Mathematical Research, 1(2), 206-212 (2012).
[5] Degtyarev, L.M., Nakhan’kov, V.G., and Rudakov, L.I., Dynamics of the formation and interaction of Langmuir solitons and strong turbulence, Zh. Eksp. Teor. Fiz., 67, 533-542 (1974).
[6] Degtyarev, L.M., Zakharov, V.E., Sagdeev, R.Z., Solov’ev, G.I., Shapiro, V.D., Shevchenko, V.I., Langmuir collapse under pumping and wave energy dissipation, Zh. Eksp. Teor. Fiz., 85, 1221-1231 (1983).
[7] Anisimov, S.I., Berezovskii, M.A., Ivanov, M.F., Petrov, I.V., Rubenchick, A.M., Zakharov, V.E., Computer simulation of the Langmuir collapse, Phys. Lett. A, 92(1), 32-34 (1982).
[8] Anisimov, S.I., Berezovskii, M.A., Zakharov, V.E., Petrov, I.V., Rubenchik, A.M., Numerical simulation of a Langmuir collapse, Zh. Eksp. Teor. Fiz., 84, 2046-2054 (1983).
[9] D’yachenko, A.I., Zakharov, V.E., Rubenchik, A.M., Sagdeev, R.Z., Shvets, V.F., Numerical simulation of two-dimensional Langmuir collapse, Zh. Eksp. Teor. Fiz., 94, 144-155 (1988).
[10] Zakharov, V.E., Pushkarev, A.N., Rubenchik, A.M., Sagdeev, R.Z., Shvets, V.F., Numerical simulation of three-dimensional Langmuir collapse in plasma, Pis'ma v Zh. Eksp. Teor. Fiz., 47, 287- 290 (1988).
[11] Benilov, E. S., Stability of plasma solitons, Zh. Eksp. Theor. Fiz., 88, 120-128 (1985).
[12] Zakharov, V.E., Pushkarev, A.N., Sagdeev, R.Z., Soloviev, S.I., Shapiro, V.D., Shvets, V.F., Shevchenko, V.I., “Throughout” modelling of the one-dimensional Langmuir turbulence, Sov. Phys. Dokl. 34, 248-251 (1989).
[13] Dyachenko, A.I., Pushkarev, A.N., Rubenchik, A.M., Sagdeev, R.Z., Shvets, V.F., Zakharov, V.E., Computer simulation of Langmuir collapse, Physica D, 52(1), 78-102 (1991).
[14] Rubenchik, A.M., Zakharov, V.E., Strong Langmuir turbulence in laser plasma, Handbook ofPlasma Physics, Elsevier Science Publishers, 3, 335-360 (1991).
[15] Musher, S.L., Rubenchik, A.M., Zakharov, V.E., Weak Langmuir turbulence, Phys. Rep. 252(4), 178-274 (1995).
[16] Robinson, P.A., Willes, A.J., and Cairns, I.H., Dynamics of Langmuir and ion-sound waves in type III solar radio sources, The Astrophysical Journal, 408, 720-734 (1993).
[17] Chen, Y-H, Lu, W., and Wang, W-H, The Nonlinear Langmuir Waves in a Multi-ionComponent Plasma, Commun. Theor. Phys., 35, 223-228 (2001).
[18] Soucek, J., Krasnoselskikh, V., Dudok de Wit, T., Pickett, J., and Kletzing, C., Nonlinear decay of foreshock Langmuir waves in the presence of plasma inhomogeneities: Theory and Cluster observations, Journal of Geophysical Research, 110, A08102:1-10 (2005).
[19] Dodin, I.Y., Geyko V.I., and Fisch, N.J., Langmuir wave linear evolution in inhomogeneous nonstationary anisotropic plasma, Physics of Plasmas, 16, 112101:1-9 (2009).
[20] Zaslavsky, A., Volokitin, A.S., Krasnoselskikh, V.V., Maksimovic M., and Bale, S.D., Spatial localization of Langmuir waves generated from an electron beam propagating in an inhomogeneous plasma: Applications to the solar wind, Journal of Geophysical Research, 115, A08103:1-11 (2010).
[21] Ratcliffe, H., Brady, C.S., Che Rozenan, M.B., and Nakariakov, V.M., A comparison of weakturbulence and particle-in-cell simulations of weak electron-beam plasma interaction, AIP-Physics of Plasmas, 21, 122104:1-9 (2014).
[22] Ajima, N.Y., and Wa, M.O., Formation and Interaction of Sonic-Langmuir Solitons, Progress of Theoretical Physics, 56(6), 1719-1739 (1976).
[23] Zakharov, V.E., Collapse of Langmuir Waves, Zh. Eksp. Teor. Fiz., 62, 1745-1759 (1972).
[24] Tuluce Demiray, S., Pandir, Y., and Bulut, H., New Soliton Solutions for Sasa-Satsuma Equation, Waves in Random and Complex Media, 25(3) , 417-428 (2015).
[25] Tuluce Demiray, S., Pandir, Y., and Bulut, H., New Solitary Wave Solutions of Maccari System, Ocean Engineering, 103, 153-159 (2015).
[26] Tuluce Demiray, S., and Bulut, H., New Exact Solutions of the New Hamiltonian Amplitude Equation and Fokas Lenells Equation, Entropy, 17, 6025-6043 (2015).
[27] Tuluce Demiray, S., Pandir, Y., and Bulut, H., All Exact Travelling Wave Solutions of Hirota Equation and Hirota-Maccari System, Optik, 127, 1848-1859 (2016).
[28] Tuluce Demiray, S., and Bulut, H., Generalized Kudryashov method for nonlinear fractional doublesinh-Poisson equation, J. Nonlinear Sci. Appl., 9, 1349-1355 (2016).
[29] Tuluce Demiray, S., Pandir, Y., and Bulut, H., The Analysis of The Exact Solutions of The Space Fractional Coupled KD Equations, AIP Conference Proceedings, 1648, 370013-(1-5) (2015)