Exact Analytical Solutions of the Perturbed Gerdjikov–Ivanov Equation via the Extended Auxiliary Equation Method.

Συγγραφείς: Naimh, Ali Hussein, Abbas, Abbas Allawi Haboob, Salameh, Ali Abdul Hassan

Πηγή: REMAH Journal. 2026, Vol. 3 Issue 170, p269-285. 17p.

Θεματικοί όροι: Nonlinear evolution equations, Analytical solutions, Plasma physics, Nonlinear optics, Elliptic functions, Theory of wave motion

A Streamlined Analytical Approach for Exact Solutions and Chaotic Dynamics in Two Higher-Dimensional Nonlinear Models.

Συγγραφείς: Shi, Yapeng¹ (AUTHOR), Feng, Yuqiang¹ (AUTHOR), Yu, Jicheng² (AUTHOR) yjicheng@126.com

Πηγή: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Oct2026, Vol. 36 Issue 13, p1-17. 17p.

Θεματικοί όροι: *Nonlinear evolution equations, *Chaos theory, *Lyapunov exponents, *Solitons, *Nonlinear wave equations, *Analytical solutions

Exact solutions to the variable-coefficient Bogoyavlensky-Konopelchenko equation by using two newly expanded methods.

Συγγραφείς: Sharif, Bahzad Ali M.¹, Ali, Karmina K.¹

Πηγή: Mathematics in Engineering, Science & Aerospace (MESA). 2026, Vol. 17 Issue 3, p909-921. 13p.

Θεματικοί όροι: *Nonlinear evolution equations, *Solitons, *Fluid dynamics, *Analytical solutions, *Nonlinear wave equations

Physics-informed neural networks with Riccati-type pseudopotential constraints for solving nonlinear evolution equations.

Συγγραφείς: Wan, Junchao¹ (AUTHOR), Wang, Hui¹ (AUTHOR) yhwang_smu@163.com, Wang, Yunhu^1,2 (AUTHOR)

Πηγή: Chaos. Sep2026, Vol. 36 Issue 9, p1-13. 13p.

Θεματικοί όροι: *Nonlinear evolution equations, *Pseudopotential method, *Integrable systems, *Solitons, *Nonlinear Schrödinger equation, *Korteweg-de Vries equation

A direct PinT algorithm for higher-order nonlinear time-evolution equations.

Συγγραφείς: Zhong, Shun-Zhi¹ (AUTHOR) szzhongm@sina.com, Zhao, Yong-Liang¹ (AUTHOR) ylzhaofde@sina.com, Shu, Qian-Yu¹ (AUTHOR) shuqy@sicnu.edu.cn

Πηγή: Applied Numerical Mathematics. Sep2026, Vol. 227, p25-41. 17p.

Θεματικοί όροι: *Nonlinear evolution equations, *Parallel algorithms, *Matrix decomposition, *Numerical analysis, *Autonomous differential equations, *Chebyshev polynomials, *Eigenanalysis

The Cauchy problem of the Hartree equation in Dunkl setting.

Συγγραφείς: Deng, Qingquan¹ (AUTHOR), Li, Ji² (AUTHOR), Long, Xiuhong³ (AUTHOR) xiuhonglong@mails.ccnu.edu.cn

Πηγή: Applicable Analysis. Sep2026, Vol. 105 Issue 14, p3144-3175. 32p.

Θεματικοί όροι: *Initial value problems, *Nonlinear evolution equations, *Uniqueness (Mathematics), *Scattering (Physics), *Differential operators, *Partial differential equations

Weakly inhomogeneous solutions to a nonlinear Vlasov–Fokker–Planck equation in a domain.

Συγγραφείς: Song, Sihyun¹ (AUTHOR) ssong@yonsei.ac.kr

Πηγή: Analysis & Applications. Aug2026, p1-94. 94p.

Θεματικοί όροι: *Fokker-Planck equation, *Nonlinear evolution equations, *Partial differential equations, *Stability theory, *Exponential decay law

Closed-form wave solutions to the van der Waals model arising in nature and the longitudinal wave motion equation in a magneto-electro-elastic circular rod.

Συγγραφείς: Wu, Fengxia¹ (AUTHOR) fengxia-0408@163.com, Alam, Md Nur^2,3 (AUTHOR) nuralam.pstu23@gmail.com, Baskonus, Haci Mehmet⁴ (AUTHOR) hmbaskonus@gmail.com, Rezazadeh, Hadi⁵ (AUTHOR) rezazadehadi1363@gmail.com

Πηγή: International Journal of Geometric Methods in Modern Physics. Aug2026, Vol. 23 Issue 9, p1-23. 23p.

Θεματικοί όροι: *Nonlinear evolution equations, *Longitudinal waves, *Wave equation, *Equations of state, *Nonlinear wave equations, *Scientific method, *Phase separation

The topological structure of solution sets and approximate controllability for semilinear evolution problems with non-compact semigroups.

Συγγραφείς: Liang, Yixing¹ (AUTHOR), Fan, Zhenbin² (AUTHOR) zbfan@yzu.edu.cn, Li, Gang² (AUTHOR)

Πηγή: International Journal of Control. Aug2026, Vol. 99 Issue 8, p2477-2497. 21p.

Θεματικοί όροι: *Nonlinear evolution equations, *Controllability in systems engineering, *Topology, *Linear operators, *Fixed point theory

Global Well-Posedness for Nonlinear Evolution Equations with a Composite Diamond Klein-Gordon Operator.

Συγγραφείς: Bupasiri, Sudprathai¹ sudprathai@gmail.com

Πηγή: IAENG International Journal of Applied Mathematics. Aug2026, Vol. 56 Issue 8, p2991-2995. 5p.

Θεματικοί όροι: *Nonlinear evolution equations, *Differential operators, *Hyperbolic differential equations, *Mathematical analysis, *Sobolev spaces, *Functional analysis

NEW SOLITARY WAVES OF STOCHASTIC (3+1)-DIMENSIONAL NONLINEAR EVOLUTION EQUATIONS UNDER BROWNIAN MOTION.

Συγγραφείς: FARYAD, UROOSA¹ (AUTHOR), FARYAD, AQSA² (AUTHOR), ALDAYEL, IBRAHIM³ (AUTHOR), KHAN, MERAJ ALI³ (AUTHOR) mskhan@imamu.edu.sa, AKGÜL, ALI⁴ (AUTHOR)

Πηγή: Fractals. 2026, Vol. 34 Issue 6, p1-13. 13p.

Θεματικοί όροι: *Brownian motion, *Nonlinear evolution equations, *Riccati equation, *Scientific method, *Solitons, *Stochastic processes, *Fluid mechanics, *Plasma physics

On the Invariant Subspace Method for Nonlinear Second-Order Evolution Equations.

Συγγραφείς: Badgaish, Manal¹ (AUTHOR), Hmidouch, Lhoucine² (AUTHOR), Hmidouch, Nacir³ (AUTHOR) nhmidouch@talladega.edu

Πηγή: Mathematics (2227-7390). Jun2026, Vol. 14 Issue 12, p2155. 14p.

Θεματικοί όροι: *Invariant subspaces, *Nonlinear evolution equations, *Ordinary differential equations, *Reduced-order models, *Transport equation, *Reaction-diffusion equations, *Analytical solutions

Inelastic lump–breather interactions and periodic wave dynamics in the generalized Calogero–Bogoyavlenskii–Schiff equation via a bilinear neural architecture.

Συγγραφείς: Akram, Sonia¹ (AUTHOR) soniaakram641@gmal.com, Rahman, Mati ur² (AUTHOR) mrmahman@imamu.edu.sa, AL-Essa, Laila A.³ (AUTHOR) Laalessa@pnu.edu.sa

Πηγή: European Physical Journal: Special Topics. Jun2026, Vol. 235 Issue 8, p2019-2038. 20p.

Θεματικοί όροι: *Nonlinear wave equations, *Nonlinear evolution equations, *Nonlinear waves, *Symbolic computation, *Coherent structures

INFINITE EXACT SOLUTIONS FOR THE WAVE EQUATION OF NONLINEAR ELASTIC ROD.

Συγγραφείς: GUO, PENG¹ guopenglzjtu@126.com, WU, XIANG^2,3 wuxiang@mail.lzjtu.cn, SUN, XIAO-WEI^1,3 sunxw@lzjtu.edu.cn, WANG, LIANG-BI^3,4 lbiwang@yeah.net

Πηγή: Journal of Science & Arts. Jun2026, Vol. 26 Issue 2, p303-314. 12p.

Θεματικοί όροι: *Wave equation, *Nonlinear evolution equations, *Analytical solutions, *Solitons, *Scientific method, *Simulation software

Weyl Double-Measure Pseudo Almost Automorphic Solutions to a Semilinear Abstract Differential Equation.

Συγγραφείς: Li, Yongkun¹ (AUTHOR) yklie@ynu.edu.cn

Πηγή: Bulletin of the Iranian Mathematical Society. Jun2026, Vol. 52 Issue 3, p1-34. 34p.

Θεματικοί όροι: *Nonlinear evolution equations, *Mathematical functions, *Exponential stability, *Uniqueness (Mathematics)

ON A METHOD FOR SOLVING THE INITIAL-BOUNDARY VALUE PROBLEM FOR THE GARDNER EQUATION.

Συγγραφείς: Bezrodnykh, S. I.¹ (AUTHOR) sbezrodnykh@mail.ru, Pikulin, S. V.¹ (AUTHOR) spikulin@gmail.com

Πηγή: Journal of Mathematical Sciences. May2026, Vol. 299 Issue 2, p121-136. 16p.

Θεματικοί όροι: *Nonlinear evolution equations, *Numerical analysis, *Solitons, *Time integration scheme, *Algorithms, *Initial value problems, *Nonlinear waves

Existence and Regularity of Solutions to Elastic Systems With Nonlocal Conditions.

Συγγραφείς: Gou, Haide¹ (AUTHOR) gouhaide@nwnu.edu.cn, Yang, Shenghe¹ (AUTHOR)

Πηγή: Mathematical Methods in the Applied Sciences. 5/15/2026, Vol. 49 Issue 7, p6726-6752. 27p.

Θεματικοί όροι: *Nonlinear evolution equations, *Fixed point theory, *Boundary value problems, *Elastic structures (Mechanics), *Banach spaces

The analytical solutions of the Sharma–Tasso–Olver–Burgers equation using improved sub-equation method.

Συγγραφείς: Arslantürk, Reyhan¹ (AUTHOR) reyhanarslanturk52@gmail.com, Durur, Hülya² (AUTHOR) hulyadurur@ardahan.edu.tr

Πηγή: Modern Physics Letters B. 5/10/2026, Vol. 40 Issue 13, p1-24. 24p.

Θεματικοί όροι: *Analytical solutions, *Nonlinear evolution equations, *Traveling waves (Physics), *Solitons, *Plasma physics, *Shock waves, *Fluid mechanics

Tails from the bulk: gravitational decay in AdS5.

Συγγραφείς: Crump, John R. V.¹ (AUTHOR) jrvc2@cam.ac.uk, Santos, Jorge E.¹ (AUTHOR) jss55@cam.ac.uk

Πηγή: Journal of High Energy Physics. May2026, Vol. 2026 Issue 5, p1-34. 34p.

Θεματικοί όροι: *Schwarzschild black holes, *Nonlinear evolution equations, *WKB approximation, *Perturbation theory, *Damping (Mechanics)

Soliton structures and dynamical coexistence phenomena in the Shynaray-IIA nonlinear evolution equation.

Συγγραφείς: Chou, Dean^1,2 (AUTHOR), Ur Rehman, Hamood^3,4 (AUTHOR), Iqbal, Ifrah⁴ (AUTHOR), Allahyani, Seham Ayesh⁵ (AUTHOR), Gusu, Daba Meshesha⁶ (AUTHOR) daba.meshesha@ambou.edu.et

Πηγή: Optical & Quantum Electronics. May2026, Vol. 58 Issue 5, p1-21. 21p.

Θεματικοί όροι: *Nonlinear evolution equations, *Solitons, *Chaos theory, *Nonlinear optics, *Wave equation, *Optical fiber communication