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Exp-function method for nonlinear wave equations

Citations

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Cited by:

  1. Iqbal, Muhammad S. & Seadawy, Aly R. & Baber, Muhammad Z. & Qasim, Muhammad, 2022. "Application of modified exponential rational function method to Jaulent–Miodek system leading to exact classical solutions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
  2. Bekir, Ahmet, 2009. "The tanh–coth method combined with the Riccati equation for solving non-linear equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1467-1474.
  3. Bekir, Ahmet & Cevikel, Adem C., 2009. "New exact travelling wave solutions of nonlinear physical models," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1733-1739.
  4. Javidi, M. & Golbabai, A., 2009. "A new domain decomposition algorithm for generalized Burger’s–Huxley equation based on Chebyshev polynomials and preconditioning," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 849-857.
  5. Tao, Zhao-Ling, 2009. "Frequency–amplitude relationship of nonlinear oscillators by He’s parameter-expanding method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 642-645.
  6. Zeng, Xiping & Dai, Zhengde & Li, Donglong, 2009. "New periodic soliton solutions for the (3+1)-dimensional potential-YTSF equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 657-661.
  7. Akinyemi, Lanre & Şenol, Mehmet & Iyiola, Olaniyi S., 2021. "Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 211-233.
  8. Kumar, Sachin & Kumar, Dharmendra & Kumar, Amit, 2021. "Lie symmetry analysis for obtaining the abundant exact solutions, optimal system and dynamics of solitons for a higher-dimensional Fokas equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
  9. Bekir, Ahmet & Boz, Ahmet, 2009. "Application of Exp-function method for (2+1)-dimensional nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 458-465.
  10. Javidi, M. & Golbabai, A., 2009. "Modified homotopy perturbation method for solving non-linear Fredholm integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1408-1412.
  11. 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.
  12. Sheng Zhang & Yuanyuan Wei & Bo Xu, 2019. "Fractional Soliton Dynamics and Spectral Transform of Time-Fractional Nonlinear Systems: A Concrete Example," Complexity, Hindawi, vol. 2019, pages 1-9, August.
  13. Nur Alam & Fethi Bin Muhammad Belgacem, 2016. "Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ))-Expansion Method Implementation," Mathematics, MDPI, vol. 4(1), pages 1-13, February.
  14. Jiong Weng & Xiaojing Liu & Youhe Zhou & Jizeng Wang, 2021. "A Space-Time Fully Decoupled Wavelet Integral Collocation Method with High-Order Accuracy for a Class of Nonlinear Wave Equations," Mathematics, MDPI, vol. 9(22), pages 1-17, November.
  15. Ali, A.H.A. & Raslan, K.R., 2009. "Variational iteration method for solving partial differential equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1520-1529.
  16. Hassan Kamil Jassim & Mohammed Abdulshareef Hussein, 2023. "A New Approach for Solving Nonlinear Fractional Ordinary Differential Equations," Mathematics, MDPI, vol. 11(7), pages 1-13, March.
  17. Erbaş, Barış & Yusufoğlu, Elçin, 2009. "Exp-function method for constructing exact solutions of Sharma–Tasso–Olver equation," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2326-2330.
  18. Sheng Zhang & Lijie Zhang & Bo Xu, 2019. "Rational Waves and Complex Dynamics: Analytical Insights into a Generalized Nonlinear Schrödinger Equation with Distributed Coefficients," Complexity, Hindawi, vol. 2019, pages 1-17, March.
  19. Ma, Wen-Xiu & Lee, Jyh-Hao, 2009. "A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1356-1363.
  20. Abdel-Gawad, Hamdy I. & Abdel-Gawad, Ahmed H., 2021. "Discrete and continuum models of COVID-19 virus, formal solutions, stability and comparison with real data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 222-230.
  21. Nguyen, Lu Trong Khiem, 2015. "Modified homogeneous balance method: Applications and new solutions," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 148-155.
  22. Tariq, Kalim U. & Bekir, Ahmet & Nisar, Sana, 2023. "The dynamical structures of the Sharma–Tasso–Olver model in doubly dispersive medium," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
  23. Tariq, Hira & Akram, Ghazala, 2017. "New approach for exact solutions of time fractional Cahn–Allen equation and time fractional Phi-4 equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 352-362.
  24. Sheng Zhang & Siyu Hong, 2017. "Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System," Complexity, Hindawi, vol. 2017, pages 1-10, November.
  25. 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.
  26. Xiaoming Wang & Shehbaz Ahmad Javed & Abdul Majeed & Mohsin Kamran & Muhammad Abbas, 2022. "Investigation of Exact Solutions of Nonlinear Evolution Equations Using Unified Method," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
  27. Xu, Lan, 2008. "Variational approach to solitons of nonlinear dispersive K(m,n) equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 137-143.
  28. Zhou, Jiangrui & Zhou, Rui & Zhu, Shihui, 2020. "Peakon, rational function and periodic solutions for Tzitzeica–Dodd–Bullough type equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
  29. Khaled A. Gepreel, 2020. "Analytical Methods for Nonlinear Evolution Equations in Mathematical Physics," Mathematics, MDPI, vol. 8(12), pages 1-14, December.
  30. Varatharajan, N. & DasGupta, Anirvan, 2016. "The effect of perturbed advection on a class of solutions of a non-linear reaction-diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 33-45.
  31. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
  32. Khani, F., 2009. "Analytic study on the higher order Ito equations: New solitary wave solutions using the Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2128-2134.
  33. Lingxiao Li & Mingliang Wang & Jinliang Zhang, 2022. "Application of Generalized Logistic Function to Travelling Wave Solutions for a Class of Nonlinear Evolution Equations," Mathematics, MDPI, vol. 10(21), pages 1-13, October.
  34. M. Ali Akbar & Md. Nur Alam & Md. Golam Hafez, 2016. "Application of the novel (G′/G)-expansion method to construct traveling wave solutions to the positive Gardner-KP equation," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(1), pages 85-96, March.
  35. Sheng Zhang & Jiao Gao & Bo Xu, 2022. "An Integrable Evolution System and Its Analytical Solutions with the Help of Mixed Spectral AKNS Matrix Problem," Mathematics, MDPI, vol. 10(21), pages 1-16, October.
  36. Patra, A. & Baliarsingh, P. & Dutta, H., 2022. "Solution to fractional evolution equation using Mohand transform," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 557-570.
  37. Muhammad Shakeel & Attaullah & Essam Roshdy El-Zahar & Nehad Ali Shah & Jae Dong Chung, 2022. "Generalized Exp-Function Method to Find Closed Form Solutions of Nonlinear Dispersive Modified Benjamin–Bona–Mahony Equation Defined by Seismic Sea Waves," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
  38. Jing Chang & Jin Zhang & Ming Cai, 2021. "Series Solutions of High-Dimensional Fractional Differential Equations," Mathematics, MDPI, vol. 9(17), pages 1-21, August.
  39. Younis, Muhammad & Rizvi, Syed Tahir Raza & Ali, Safdar, 2015. "Analytical and soliton solutions: Nonlinear model of nanobioelectronics transmission lines," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 994-1002.
  40. Abourabia, A.M. & Morad, A.M., 2015. "Exact traveling wave solutions of the van der Waals normal form for fluidized granular matter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 333-350.
  41. Mahmoud, Abeer A. & Tolba, R.E., 2019. "Nonlinear dust-acoustic waves due to the interaction of streaming protons and electrons with dusty plasma," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 320-327.
  42. Akbar, Yasir & Afsar, Haleem & Abbas, Shahzad & Javed, Muhammad Waqas & Ullah, Najib, 2021. "Dromions for the coupled Maccari’s system in fluid mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
  43. Suheel Abdullah Malik & Ijaz Mansoor Qureshi & Muhammad Amir & Aqdas Naveed Malik & Ihsanul Haq, 2015. "Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-15, March.
  44. Soliman, A.A., 2009. "Exact solutions of KdV–Burgers’ equation by Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1034-1039.
  45. Bo Xu & Sheng Zhang, 2022. "Analytical Method for Generalized Nonlinear Schrödinger Equation with Time-Varying Coefficients: Lax Representation, Riemann-Hilbert Problem Solutions," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
  46. Golbabai, A. & Javidi, M., 2009. "A spectral domain decomposition approach for the generalized Burger’s–Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 385-392.
  47. Alejandro León-Ramírez & Oswaldo González-Gaxiola & Guillermo Chacón-Acosta, 2023. "Analytical Solutions to the Chavy-Waddy–Kolokolnikov Model of Bacterial Aggregates in Phototaxis by Three Integration Schemes," Mathematics, MDPI, vol. 11(10), pages 1-24, May.
  48. 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.
  49. EL Achab, Abdelfattah, 2020. "On the integrability of the generalized Pochhammer–Chree (PC) equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
  50. Aly R. Seadawy & Syed T. R. Rizvi & Hanadi Zahed, 2023. "Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficien," Mathematics, MDPI, vol. 11(5), pages 1-16, February.
  51. (Benn)Wu, Xu-Hong & He, Ji-Huan, 2008. "EXP-function method and its application to nonlinear equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 903-910.
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