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

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  1. 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).
  2. Nickel, J., 2007. "Travelling wave solutions to the Kuramoto–Sivashinsky equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1376-1382.
  3. 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.
  4. 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.
  5. 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.
  6. 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).
  7. 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.
  8. 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.
  9. Kudryashov, N.A. & Lavrova, S.F., 2021. "Dynamical features of the generalized Kuramoto-Sivashinsky equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
  10. 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.
  11. 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).
  12. 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.
  13. 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).
  14. 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.
  15. 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).
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
  27. Kudryashov, Nikolay A., 2020. "Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 371(C).
  28. 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.
  29. 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).
  30. Kudryashov, Nikolay A., 2020. "First integrals and general solution of the complex Ginzburg-Landau equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
  31. 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.
  32. 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.
  33. Ranković, Dragana & Zdravković, Slobodan, 2022. "Two component model of microtubules – subsonic and supersonic solitary waves," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
  34. 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.
  35. 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.
  36. 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.
  37. Fahmy, E.S., 2008. "Travelling wave solutions for some time-delayed equations through factorizations," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1209-1216.
  38. 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.
  39. 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.
  40. 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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