THERMAL SCIENCE

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N-wave and other solutions to the B-type Kadomtsev-Petviashvili equation

ABSTRACT
The present article studies a B-type Kadomtsev-Petviashvili (KP) equation with certain applications in the fluids. Stating with the Hirota's bilinear form and adopting reliable methodologies, a group of exact solutions such as the N-wave and other solutions to the B-type KP equation is formally derived. Some figures in two and three dimensions are given to illustrate the characteristics of the obtained solutions. The results of the current work actually help to complete the previous studies about the B-type KP equation.
KEYWORDS
PAPER SUBMITTED: 2019-07-22
PAPER REVISED: 2019-08-29
PAPER ACCEPTED: 2019-09-02
PUBLISHED ONLINE: 2019-10-06
DOI REFERENCE: https://doi.org/10.2298/TSCI160722367I
REFERENCES
  1. Kudryashov, N.A., One method for finding exact solutions of nonlinear differential equations, Communications in Nonlinear Science and Numerical Simulations, 17 (2012), pp. 2248-2253
  2. Mirzazadeh, M., et al., 1-Soliton solution of KdV6 equation, Nonlinear Dynamics, 80 (2015), pp. 387-396
  3. Ege, S.M., Misirli, E., The modified Kudryashov method for solving some fractional-order nonlinear equations, Advances in Difference Equations, 2014 (2014), 135
  4. Hosseini, K., et al., New exact solutions of some nonlinear evolution equations of pseudoparabolic type, Optical and Quantum Electronics, 49 (2017), 241
  5. Hosseini, K., et al., New exact traveling wave solutions of the Tzitzéica-type evolution equations arising in non-linear optics, Journal of Modern Optics, 64 (2017), pp. 1688-1692
  6. Hosseini, K., et al., New exact solutions of the conformable time-fractional Cahn-Allen and Cahn-Hilliard equations using the modified Kudryashov method, Optik, 132 (2017), pp. 203-209
  7. Wazwaz, A.M., Multiple soliton solutions and rational solutions for the (2+1)-dimensional dispersive long water-wave system, Ocean Engineering, 60 (2013), pp. 95-98
  8. Wazwaz, A.M., Two B-type Kadomtsev-Petviashvili equations of (2+1) and (3+1) dimensions: Multiple soliton solutions, rational solutions and periodic solutions, Computers & Fluids, 86 (2013), pp. 357-362
  9. Wazwaz, A.M., New (3+1)-dimensional nonlinear evolution equation: multiple soliton solutions, Central European Journal of Engineering, 4 (2014), pp. 352-356
  10. Mirzazadeh, M., Topological and non-topological soliton solutions of Hamiltonian amplitude equation by He's semi-inverse method and ansatz approach, Journal of the Egyptian Mathematical Society, 23 (2015), pp. 292-296
  11. Hosseini, K., et al., Bright and singular soliton solutions of the conformable time-fractional Klein-Gordon equations with different nonlinearities, Waves in Random and Complex Media, 28 (2018), pp. 426-434
  12. Wazwaz, A.M., El-Tantawy, S.A., Solving the (3+1)-dimensional KP-Boussinesq and BKP-Boussinesq equations by the simplified Hirota's method, Nonlinear Dynamics, 88 (2017), pp. 3017-3021
  13. Wazwaz, A.M., Kaur, L., Complex simplified Hirota's forms and Lie symmetry analysis for multiple real and complex soliton solutions of the modified KdV-Sine-Gordon equation, Nonlinear Dynamics, 95 (2019), pp. 2209-2215
  14. Wazwaz, A.M., Two new integrable fourth-order nonlinear equations: multiple soliton solutions and multiple complex soliton solutions, Nonlinear Dynamics, 94 (2018), pp. 2655-2663
  15. Wazwaz, A.M., El-Tantawy, S.A., A new integrable (3+1)-dimensional KdV-like model with its multiple-soliton solutions, Nonlinear Dynamics, 83 (2016), pp. 1529-1534
  16. Wazwaz, A.M., Abundant solutions of various physical features for the (2+1)-dimensional modified KdV-Calogero-Bogoyavlenskii-Schiff equation, Nonlinear Dynamics, 89 (2017), pp. 1727-1732
  17. Zhang, L., et al., Classifying bilinear differential equations by linear superposition principle, International Journal of Modern Physics B, 30 (2016), 1640029
  18. Zhou, Y., Ma, W.X., Applications of linear superposition principle to resonant solitons and complexitons, Computers and Mathematics with Applications, 73 (2017), pp. 1697-1706
  19. Zhou, Y., Manukure, S., Complexiton solutions to the Hirota-Satsuma-Ito equation, Mathematical Methods in the Applied Sciences, 42 (2019), pp. 2344-2351
  20. Ma, W.X., et al., A multiple exp-function method for nonlinear differential equations and its application, Physica Scripta, 82 (2010), 065003
  21. Yildirim, Y., et al., A multiple exp-function method for the three model equations of shallow water waves, Nonlinear Dynamics, 89 (2017), pp. 2291-2297
  22. Liu, J.G., et al., Multiple soliton solutions for the new (2+1)-dimensional Korteweg-de Vries equation by multiple exp-function method, Applied Mathematics Letters, 80 (2018), pp. 71-78
  23. Kaur, L., Wazwaz, A.M., Lump, breather and solitary wave solutions to new reduced form of the generalized BKP equation, International Journal of Numerical Methods for Heat & Fluid Flow, 29 (2019), pp. 569-579
  24. Gao, X.Y., Bäcklund transformation and shock-wave-type solutions for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equationin fluid mechanics, Ocean Engineering, 96 (2015), pp. 245-247
  25. Peng, W.Q., et al., Analysis on lump, lumpoff and rogue waves with predictability to the (2+1)-dimensional B-type Kadomtsev-Petviashvili equation, Physics Letters A, 382 (2018), pp. 2701-2708
  26. Feng, L.L., et al., Rogue waves, homoclinic breather waves and soliton waves for the (2+1)-dimensional B-type Kadomtsev-Petviashvili equation, Applied Mathematics Letters, 65 (2017), pp. 90-97
  27. Tu, J.M., et al., On periodic wave solutions with asymptotic behaviors to a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation in fluid dynamics, Computers and Mathematics with Applications, 72 (2016), pp. 2486-2504
  28. Yan, X.W., et al., Bäcklund transformation, rogue wave solutions and interaction phenomena for a (3+1)-dimensional B-type Kadomtsev-Petviashvili-Boussinesq equation, Nonlinear Dynamics, 92 (2018), pp. 709-720
  29. Cheng, L., Zhang, Y., Multiple wave solutions and auto-Bäcklund transformation for the (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation, Computers and Mathematics with Applications, 70 (2015), pp. 765-775
  30. Cheng, L., et al., Pfaffians of B-type Kadomtsev-Petviashvili equation and complexitons to a class of nonlinear partial differential equations in (3+1) dimensions, Pramana Journal of Physics, 93 (2019), 4
  31. Wazwaz, A.M., Distinct kinds of multiple-soliton solutions for a (3+1)-dimensional generalized Btype Kadomtsev-Petviashvili equation, Physica Scripta, 84 (2011), 055006
  32. Cao, X., Lump solutions to the (3+1)-dimensional generalized b-type Kadomtsev-Petviashvili equation, Advances in Mathematical Physics, 2018 (2018), 7843498
  33. Abudiab, M., Khalique, C.M., Exact solutions and conservation laws of a (3+1)-dimensional B-type Kadomtsev-Petviashvili equation, Advances in Difference Equations, 2013 (2013), 221
  34. Darvishi, M.T., et al., Exact propagating multi-anti-kink soliton solutions of a (3+1)-dimensional Btype Kadomtsev-Petviashvili equation, Nonlinear Dynamics, 83 (2016), pp. 1453-1462
  35. Hu, W.Q., et al., Periodic wave, breather wave and travelling wave solutions of a (2+1)-dimensional B-type Kadomtsev-Petviashvili equation in fluids or plasmas, European Physical Journal Plus, 131 (2016), 390
  36. Singh, M., Gupta, R.K., Soliton and quasi-periodic wave solutions for b-type Kadomtsev-Petviashvili equation, Indian Journal of Physics, 91 (2017), pp. 1345-1354
  37. Du, X.X., et al., Lump, mixed lump-kink, breather and rogue waves for a B-type Kadomtsev-Petviashvili equation, Waves in Random and Complex Media, (2019), doi.10.1080/17455030.2019.1566681
  38. Sedeeg, A.K.H., et al., Generalized optical soliton solutions to the (3+1)-dimensional resonant nonlinear Schrödinger equation with Kerr and parabolic law nonlinearities, Optical and Quantum Electronics, 51 (2019), 173
  39. Ghanbari, B., Gómez-Aguilar, J.F., Optical soliton solutions of the Ginzburg-Landau equation with conformable derivative and Kerr law nonlinearity, Revista Mexicana de Física, 65 (2019), pp. 73-81
  40. Yépez Martínez, H., Gómez-Aguilar, J.F., Local M-derivative of order \alpha and the modified expansion function method applied to the longitudinal wave equation in a magneto electro-elastic circular rod, Optical and Quantum Electronics, 50 (2018), 375
  41. Baskonus, H.M., Gómez-Aguilar, J.F., New singular soliton solutions to the longitudinal wave equation in a magneto-electro-elastic circular rod with M-derivative, Modern Physics Letters B, 33 (2019), 1950251
  42. Ghanbari, B., Gómez-Aguilar, J.F., New exact optical soliton solutions for nonlinear Schrödinger equation with second-order spatio-temporal dispersion involving M-derivative, Modern Physics Letters B, 33 (2019), 1950235
  43. Yépez Martínez, H., Gómez-Aguilar, J.F., Optical solitons solution of resonance nonlinear Schrödinger type equation with Atangana's-conformable derivative using sub-equation method, Waves in Random and Complex Media, (2019), doi: 10.1080/17455030.2019.1603413
  44. Liu, W., et al., Analytic study on triple-S, triple-triangle structure interactions for solitons in inhomogeneous multi-mode fiber, Applied Mathematics and Computation, 361 (2019), pp. 325-331
  45. Yan, Y., Liu, W., Stable transmission of solitons in the complex cubic-quintic Ginzburg-Landau equation with nonlinear gain and higher-order effects, Applied Mathematics Letters, 98 (2019), pp. 171-176
  46. Liu, X., et al., Periodic attenuating oscillation between soliton interactions for higher-order variable coefficient nonlinear Schrödinger equation, Nonlinear Dynamics, 96 (2019), pp. 801-809
  47. Liu, W., et al., Dromion-like soliton interactions for nonlinear Schrödinger equation with variable coefficients in inhomogeneous optical fibers, Nonlinear Dynamics, 96 (2019), pp. 729-736
  48. Yang, C., et al., Bright soliton interactions in a (2+1)-dimensional fourth-order variable-coefficient nonlinear Schrödinger equation for the Heisenberg ferromagnetic spin chain, Nonlinear Dynamics, 95 (2019), pp. 983-994
  49. Liu, W., et al., Interaction properties of solitonics in inhomogeneous optical fibers, Nonlinear Dynamics, 95 (2019), pp. 557-563
  50. Hosseini, K., et al., New wave form solutions of nonlinear conformable time-fractional Zoomeron equation in (2+1)-dimensions, Waves in Random and Complex Media, (2019), doi: 10.1080/17455030.2019.1579393