Hamiltonian simulation for nonlinear partial differential equation by Schrödingerization. [PDF]
Sci RepSasaki S, Endo K, Muramatsu M.
europepmc +1 more source
From Stability to Chaos: A Complete Classification of the Damped Klein‐Gordon Dynamics
Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9696-9708, June 2026.ABSTRACT We investigate the transition between stability and chaos in the damped Klein‐Gordon equation, a fundamental model for wave propagation and energy dissipation. Using semigroup methods and spectral criteria, we derive explicit thresholds that determine when the system exhibits asymptotic stability and when it displays strong chaotic dynamics ...
Carlos Lizama +2 more
wiley +1 more source
Exact soliton, lump, and breather solutions of the (3 + 1)-dimensional Jimbo-Miwa equation via the bilinear neural network method. [PDF]
Sci RepHussein HH, Mekawey H, Elsheikh A.
europepmc +1 more source
Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9814-9831, June 2026.ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq +4 more
wiley +1 more source
Deterministic, stochastic, and mean-field PDE models in neuroscience. [PDF]
Front Comput NeurosciÇetin C +5 more
europepmc +1 more source
Theranostic Advancements in Brain Cancer: Promising Approaches for Emerging Therapy
MedComm – Oncology, Volume 5, Issue 2, June 2026.Strategies for improving intra‐arterial administration (A) and photodynamic therapy in brain cancer (B). Improving intra‐arterial (IA) administration and photodynamic therapy (PDT) for brain cancer involves enhancing tumor targeting and breaching the blood–brain barrier (BBB). Key strategies include super selective catheterization, using osmotic agents
Bipraban Khanra, Manoj Kumar Sarangi
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New analytical wave solutions for the gardner equation via the Riccati-modified extended simple equation method. [PDF]
Sci RepJawarneh Y +5 more
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An Augmented Lagrangian Preconditioner for Navier–Stokes Equations With Runge–Kutta in Time
Numerical Linear Algebra with Applications, Volume 33, Issue 3, June 2026.ABSTRACT We consider an implicit Runge–Kutta method for the numerical time integration of the nonstationary incompressible Navier–Stokes equations. This yields a sequence of nonlinear problems to be solved for the stages of the Runge–Kutta method. The resulting nonlinear system of differential equations is discretized using a finite element method.
Santolo Leveque +2 more
wiley +1 more source
Nonlinear periodic orbit solutions and their bifurcation structure at the origin of soliton hopping in coupled microresonators. [PDF]
Commun PhysDeshmukh S +4 more
europepmc +1 more source
Building a Digital Twin for Material Testing: Model Reduction and Data Assimilation
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.ABSTRACT The rapid advancement of industrial technologies, data collection, and handling methods has paved the way for the widespread adoption of digital twins (DTs) in engineering, enabling seamless integration between physical systems and their virtual counterparts.
Rubén Aylwin +5 more
wiley +1 more source