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Simplest equation method to look for exact solutions of nonlinear differential equations

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Cited by:

  1. Noha M. Rasheed & Mohammed O. Al-Amr & Emad A. Az-Zo’bi & Mohammad A. Tashtoush & Lanre Akinyemi, 2021. "Stable Optical Solitons for the Higher-Order Non-Kerr NLSE via the Modified Simple Equation Method," Mathematics, MDPI, vol. 9(16), pages 1-12, August.
  2. Mustafa Inc & Rubayyi T. Alqahtani & Ravi P. Agarwal, 2023. "W-Shaped Bright Soliton of the (2 + 1)-Dimension Nonlinear Electrical Transmission Line," Mathematics, MDPI, vol. 11(7), pages 1-13, April.
  3. Sağlam Özkan, Yeşim & Yaşar, Emrullah, 2021. "Breather-type and multi-wave solutions for (2+1)-dimensional nonlocal Gardner equation," Applied Mathematics and Computation, Elsevier, vol. 390(C).
  4. Yusuf Pandir & Halime Ulusoy, 2013. "New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations," Journal of Mathematics, Hindawi, vol. 2013, pages 1-5, January.
  5. Nickel, J., 2007. "Travelling wave solutions to the Kuramoto–Sivashinsky equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1376-1382.
  6. Oke Davies Adeyemo & Lijun Zhang & Chaudry Masood Khalique, 2022. "Bifurcation Theory, Lie Group-Invariant Solutions of Subalgebras and Conservation Laws of a Generalized (2+1)-Dimensional BK Equation Type II in Plasma Physics and Fluid Mechanics," Mathematics, MDPI, vol. 10(14), pages 1-46, July.
  7. Zayed, E.M.E. & Alurrfi, K.A.E., 2016. "Extended auxiliary equation method and its applications for finding the exact solutions for a class of nonlinear Schrödinger-type equations," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 111-131.
  8. Kudryashov, Nikolay A., 2019. "Exact solutions of the equation for surface waves in a convecting fluid," Applied Mathematics and Computation, Elsevier, vol. 344, pages 97-106.
  9. Chaudry Masood Khalique & Oke Davies Adeyemo, 2020. "Closed-Form Solutions and Conserved Vectors of a Generalized (3+1)-Dimensional Breaking Soliton Equation of Engineering and Nonlinear Science," Mathematics, MDPI, vol. 8(10), pages 1-30, October.
  10. Navickas, Z. & Telksnys, T. & Marcinkevicius, R. & Ragulskis, M., 2017. "Operator-based approach for the construction of analytical soliton solutions to nonlinear fractional-order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 625-634.
  11. Kudryashov, Nikolay A. & Ryabov, Pavel N., 2014. "Exact solutions of one pattern formation model," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1090-1093.
  12. Petar Popivanov & Angela Slavova, 2024. "Some Non-Linear Evolution Equations and Their Explicit Smooth Solutions with Exponential Growth Written into Integral Form," Mathematics, MDPI, vol. 12(7), pages 1-24, March.
  13. Andrei D. Polyanin & Alexander V. Aksenov, 2024. "Unsteady Magnetohydrodynamics PDE of Monge–Ampère Type: Symmetries, Closed-Form Solutions, and Reductions," Mathematics, MDPI, vol. 12(13), pages 1-29, July.
  14. Chaudry Masood Khalique & Karabo Plaatjie, 2021. "Symmetry Methods and Conservation Laws for the Nonlinear Generalized 2D Equal-Width Partial Differential Equation of Engineering," Mathematics, MDPI, vol. 10(1), pages 1-17, December.
  15. Nikolay A. Kudryashov & Sofia F. Lavrova, 2024. "Painlevé Analysis of the Traveling Wave Reduction of the Third-Order Derivative Nonlinear Schrödinger Equation," Mathematics, MDPI, vol. 12(11), pages 1-13, May.
  16. Yıldırım, Yakup & Yaşar, Emrullah, 2018. "A (2+1)-dimensional breaking soliton equation: Solutions and conservation laws," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 146-155.
  17. Kudryashov, Nikolay A., 2020. "Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 371(C).
  18. Andrei D. Polyanin, 2019. "Comparison of the Effectiveness of Different Methods for Constructing Exact Solutions to Nonlinear PDEs. Generalizations and New Solutions," Mathematics, MDPI, vol. 7(5), pages 1-19, April.
  19. Bruzón, M.S. & Garrido, T.M. & de la Rosa, R., 2016. "Conservation laws and exact solutions of a Generalized Benjamin–Bona–Mahony–Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 578-583.
  20. Zdravković, S. & Zeković, S. & Bugay, A.N. & Petrović, J., 2021. "Two component model of microtubules and continuum approximation," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
  21. Kudryashov, Nikolay A., 2020. "First integrals and general solution of the complex Ginzburg-Landau equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
  22. Kudryashov, Nikolay A. & Zakharchenko, Anastasia S., 2014. "Painlevé analysis and exact solutions for the Belousov–Zhabotinskii reaction–diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 111-117.
  23. Xu, Guoan & Zhang, Yi & Li, Jibin, 2022. "Exact solitary wave and periodic-peakon solutions of the complex Ginzburg–Landau equation: Dynamical system approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 157-167.
  24. Innocent Simbanefayi & Chaudry Masood Khalique, 2020. "Group Invariant Solutions and Conserved Quantities of a (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
  25. Piao, Xiangfan & Kim, Philsu, 2021. "Comment on: “The modified extended tanh-function method for solving Burgers-type equations” [Physica A 361 (2006) 394–404]," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 569(C).
  26. Kudryashov, Nikolay A. & Zakharchenko, Anastasia S., 2015. "Analytical properties and exact solutions of the Lotka–Volterra competition system," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 219-228.
  27. Ramírez, J. & Romero, J.L. & Muriel, C., 2016. "Reductions of PDEs to second order ODEs and symbolic computation," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 122-136.
  28. Ranković, Dragana & Zdravković, Slobodan, 2022. "Two component model of microtubules – subsonic and supersonic solitary waves," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
  29. Kudryashov, N.A. & Lavrova, S.F., 2021. "Dynamical features of the generalized Kuramoto-Sivashinsky equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
  30. Vitanov, Nikolay K. & Dimitrova, Zlatinka I. & Vitanov, Kaloyan N., 2015. "Modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations: further development of the methodology with applications," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 363-378.
  31. Kudryashov, Nikolay A. & Ivanova, Yulia S., 2016. "Painleve analysis and exact solutions for the modified Korteweg–de Vries equation with polynomial source," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 377-382.
  32. Vitanov, Nikolay K. & Dimitrova, Zlatinka I. & Ivanova, Tsvetelina I., 2017. "On solitary wave solutions of a class of nonlinear partial differential equations based on the function 1/coshn(αx+βt)," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 372-380.
  33. Navickas, Z. & Ragulskis, M. & Telksnys, T., 2016. "Existence of solitary solutions in a class of nonlinear differential equations with polynomial nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 333-338.
  34. Sugati, Taghreed G. & Seadawy, Aly R. & Alharbey, R.A. & Albarakati, W., 2022. "Nonlinear physical complex hirota dynamical system: Construction of chirp free optical dromions and numerical wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
  35. Kudryashov, N.A., 2015. "On nonlinear differential equation with exact solutions having various pole orders," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 173-177.
  36. Fahmy, E.S., 2008. "Travelling wave solutions for some time-delayed equations through factorizations," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1209-1216.
  37. Eslami, Mostafa, 2016. "Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 141-148.
  38. Yang, Lijuan & Du, Xianyun & Yang, Qiongfen, 2016. "New variable separation solutions to the (2 + 1)-dimensional Burgers equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1271-1275.
  39. Aksoy, Abdullah & Yenikaya, Sibel, 2023. "Soliton wave parameter estimation with the help of artificial neural network by using the experimental data carried out on the nonlinear transmission line," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
  40. A. Kudryashov, Nikolay, 2016. "On solutions of generalized modified Korteweg–de Vries equation of the fifth order with dissipation," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 39-45.
  41. Ranković, Dragana & Sivčević, Vladimir & Batova, Anna & Zdravković, Slobodan, 2023. "Three kinds of W-potentials in nonlinear biophysics of microtubules," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
  42. Chaudry Masood Khalique & Karabo Plaatjie, 2021. "Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation," Mathematics, MDPI, vol. 9(12), pages 1-17, June.
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