On the Extended Simple Equations Method (SEsM) and Its Application for Finding Exact Solutions of the Time-Fractional Diffusive Predator–Prey System Incorporating an Allee Effect by Elena V. Nikolova

“…In this paper, I extend the Simple Equations Method (SEsM) and adapt it to obtain exact solutions of systems of fractional nonlinear partial differential equations (FNPDEs). …”
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Soliton solutions, bifurcations, and sensitivity analysis to the higher-order nonlinear fractional Schrödinger equation in optical fibers by Md. Al Amin, M. Ali Akbar, M. Ashrafuzzaman Khan, Md. Sagib

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The (2+1)-Dimensional Chiral Nonlinear Schrödinger Equation: Extraction of Soliton Solutions and Sensitivity Analysis by Ejaz Hussain, Yasir Arafat, Sandeep Malik, Fehaid Salem Alshammari

“…The objective of this manuscript is to investigate the (2+1)-dimensional Chiral nonlinear Schrödinger equation (CNLSE). We employ the traveling wave transformation to convert the nonlinear partial differential equation (NLPDE) into the nonlinear ordinary differential equation (NLODE). …”
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Capturing Discontinuities with Precision: A Numerical Exploration of 3D Telegraph Interface Models via Multi-Resolution Technique by Khawaja Shams Ul Haq, Muhammad Asif, Muhammad Faheem, Ioan-Lucian Popa

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Effective Analytical Computational Technique for Conformable Time-Fractional Nonlinear Gardner Equation and Cahn-Hilliard Equations of Fourth and Sixth Order Emerging in Dispersive... by Mohammed Al-Smadi, Shrideh Al-Omari, Yeliz Karaca, Shaher Momani

“…From a numerical viewpoint, the simulations and results declare that the proposed iterative algorithm is indeed straightforward and appropriate with efficiency for long-wavelength solutions of nonlinear partial differential equations.…”
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Nonstationary Equations for the Reaction Layer with the Degenerate Equilibrium Points by Aleksei A. Bykov, Kristina E. Ermakova

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Stochastic Differential Games and a Unified Forward–Backward Coupled Stochastic Partial Differential Equation with Lévy Jumps by Wanyang Dai

“…We establish a relationship between stochastic differential games (SDGs) and a unified forward–backward coupled stochastic partial differential equation (SPDE) with discontinuous Lévy Jumps. …”
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Comparison of Different Approaches to Construct First Integrals for Ordinary Differential Equations by Rehana Naz, Igor Leite Freire, Imran Naeem

“…Different approaches to construct first integrals for ordinary differential equations and systems of ordinary differential equations are studied here. …”
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New exact soliton wave solutions appear in optical fibers with Sardar sub equation and new auxiliary equation techniques by Umair Asghar, Muhammad Imran Asjad, Yasser Salah Hamed, Ali Akgul, Murad Khan Hassani

“…These methods are applied to derive a wide range of soliton solutions for nonlinear partial differential equations. By transforming the original partial differential equation into an ordinary differential equation using an appropriate transformation, various types of solitary wave solutions are obtained. …”
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Temperature Effects on Nonlinear Vibration Behaviors of Euler-Bernoulli Beams with Different Boundary Conditions by Yaobing Zhao, Chaohui Huang

“…By using the extended Hamilton’s principle, the mathematical model which takes into account thermal and mechanical loadings, represented by partial differential equations (PDEs), is established. …”
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The Analysis of Fractional-Order Nonlinear Systems of Third Order KdV and Burgers Equations via a Novel Transform by A. A. Alderremy, Shaban Aly, Rabia Fayyaz, Adnan Khan, Rasool Shah, Noorolhuda Wyal

“…In this article, we solve nonlinear systems of third order KdV Equations and the systems of coupled Burgers equations in one and two dimensions with the help of two different methods. …”
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On the Role of Diffusion Behaviors in Stability Criterion for p-Laplace Dynamical Equations with Infinite Delay and Partial Fuzzy Parameters under Dirichlet Boundary Value by Ruofeng Rao, Zhilin Pu, Shouming Zhong, Jialin Huang

“…Different from many previous related literatures, the nonlinear p-Laplace diffusion item plays its role in the new criterion though the nonlinear p-Laplace presents great difficulties. …”
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Novel Soliton Solutions for the (3 + 1)-Dimensional Sakovich Equation Using Different Analytical Methods by Khalid K. Ali, Salman A. AlQahtani, M. S. Mehanna, Abdul-Majid Wazwaz

“…As a consequence of this, when the two components are combined, they can be used to easily counteract the effects of nonlinearity and dispersion on the integrability of partially differential equations. …”
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Using the spectral meshless radial basis functions method for solving time fractional Burgers’ equation by S. Hajiollow, F. Zabihi

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Ring-like Bright Monster Waves in Variable-Coefficient Partially Nonlocal Coupled NLS Equations with Directional Diffraction and External Perturbations in (3+1)D by Emmanuel Yomba

“…Partially nonlocal (PNL) variable-coefficient nonlinear Schrödinger equations (NLSEs) represent a significant area of study in mathematical physics and quantum mechanics, particularly in scenarios where potential and coefficients vary spatially or temporally. …”
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Propagation of different types of nonlinear dust-acoustic waves in dusty plasma in Jupiter's magnetosphere: a bifurcation analysis by R. E. Tolba, N. S. Alharthi

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Reinforcement Learning for Stability-Guaranteed Adaptive Optimal Primary Frequency Control of Power Systems Using Partially Monotonic Neural Networks by Hamad Alduaij, Yang Weng

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RETRACTED ARTICLE: Partial differential equations of entropy analysis on ternary hybridity nanofluid flow model via rotating disk with hall current and electromagnetic radiative in... by Khalid Fanoukh Al Oweidi, Faisal Shahzad, Wasim Jamshed, Usman, Rabha W. Ibrahim, El Sayed M. Tag El Din, Afrah M. AlDerea

“…For a number of significant physical characteristics, the physical situation is represented utilizing the boundary layer investigation, which produces partial differential equations (PDEs). The rheology of the movement is extended and computed in a revolving setting under the assumption that the movement is caused by a rotatingfloppy. …”
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Signature of conservation laws and solitary wave solution with different dynamics in Thomas–Fermi plasma: Lie theory by Marriam Fayyaz, Muhammad Bilal Riaz, Muhammad Junaid U Rehman, Osman Tunç

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On the analytical soliton-like solutions to (2+1)-dimensional fractional asymmetric Nizhnik-Novikov-Veselov system arising in incompressible fluids by Humaira Yasmin, Humaira Yasmin, Albandari W. Alrowaily, Mounirah Areshi, Rasool Shah, S. A. El-Tantawy, S. A. El-Tantawy

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