25 papers
This paper presents an energetics-based mathematical model for the diffusiophoretic motion of a deformable droplet on a liquid surface, deriving time-evolution equations for translation and elliptic deformation to identify three stable states and analyze the transitions between them.
This thesis investigates the dynamics and interactions of solitons (kinks, oscillons, vortices, and sphalerons) in one- and two-dimensional models by employing effective collective coordinate models to introduce radiation modes, generalize moduli space metrics with vibrational degrees of freedom, identify semi-BPS sphalerons, and propose a dynamic stabilization mechanism driven by internal modes.
This paper numerically investigates how external magnetic fields influence the long-range transport of large polarons (solitons) in discrete quasi-one-dimensional systems, demonstrating that the effect depends on both field strength and specific system parameters that define soliton properties, while also examining polarons generated by donor complexes.
This paper reports the deterministic experimental realization of breathing magnetic multi-solitons in a two-component Bose gas and demonstrates their controlled fission into fundamental constituents via a localized perturbation, effectively serving as an experimental analog of the inverse scattering transform.
Using the Whitham modulation method, this paper demonstrates that in conservative nonlinear Klein-Gordon systems, instability fronts propagate at the maximal group velocity as the solution evolves into a self-similar regime at asymptotically large times.
This paper constructs a novel family of exact cnoidal waves and dark solitons for the focusing and defocusing Ablowitz-Ladik equations, characterized by a "swinging" phase with nonlinear dependence on time and site number, derived via a two-point map that enables arbitrary lattice positioning and establishes explicit velocity quantization rules for waves on closed loops.
This paper introduces a generalized Gross-Pitaevskii equation with logarithmic density-dependent coupling to model 2D attractive Bose systems, enabling the theoretical analysis of quantum droplets, breathing modes, quench dynamics, and universal excited states while providing a robust framework for future experimental investigations.
This paper identifies a novel mechanism called "pseudo-coherence," where non-normal pseudospectral amplification in linearly stable, non-oscillatory stochastic systems drives a sharp transition to intermittent collective temporal organization and irreversible currents without requiring intrinsic oscillators or dynamical instabilities.
This paper establishes that the anomalous dispersion segment in soliton-similariton fiber lasers is the primary source of their exceptional stability and low quantum-limited noise, demonstrating through linear stability analysis and simulations that a positive stability margin in this segment directly correlates with reduced timing jitter and intensity noise.
This paper proposes the Taguchi method as an efficient optimization tool for nonlinear pulse propagation in optical fibers, demonstrating its rapid convergence and effectiveness through applications to guiding center solitons and soliton order conservation in dispersion-decreasing fibers.
This paper extends semi-classical instanton analysis to a symmetric quartic potential with four degenerate minima, deriving energy splittings and Rabi oscillations for distinct tunneling pathways that show excellent agreement with numerical results while revealing a critical coupling regime where the discrete symmetry melts into a continuous symmetry.
This paper analyzes a one-dimensional model of a self-propelled camphor disk perturbed by a second localized source, demonstrating through both numerical simulations and analytical solutions that the rotor's velocity exhibits a pronounced asymmetry depending on whether it approaches or recedes from the perturbation.
This paper establishes that for the three-dimensional degenerate compressible Navier-Stokes equations with nonlinear viscosity coefficients depending on density, smooth solutions can develop finite-time implosions at the origin provided the viscosity power-law exponent falls below a specific threshold determined by the adiabatic exponent, a result proven through novel pointwise density estimates and weighted high-order energy methods that demonstrate the viscous terms are insufficient to suppress the convective implosion mechanism.
This paper presents a framework for identifying and analyzing dynamics-induced active-inactive cluster patterns in complex networks that arise from symmetry breaking in systems with odd intrinsic dynamics and coupling, demonstrating that such patterns can exist without requiring network symmetries and providing a stability analysis based on coupling strength and intercluster weights.
This study investigates how inertial effects influence autotoxicity-mediated vegetation patterns on sloped arid terrains using a hyperbolic extension of the Klausmeier model, revealing that inertia acts as a destabilizing mechanism that enlarges the parameter range for uphill migrating bands, can induce hysteresis by reversing bifurcation regimes near onset, and increases pulse speeds in far-from-equilibrium conditions.
This paper investigates the existence and stability of Maxwell fronts—stationary interfaces between energetically equivalent states—in discrete nonlinear Schrödinger equations with competing nonlinearities (specifically quadratic-cubic and cubic-quintic terms), analyzing their persistence across weak and strong coupling regimes through linear stability and exponential asymptotic techniques.
This paper investigates the spectral and dynamical properties of the fractional nonlinear Schrödinger equation under harmonic confinement, revealing how the fractional order fundamentally reshapes the stability and evolution of stationary states and leads to distinct dynamical regimes in focusing and defocusing scenarios.
This paper introduces a dynamical mean-field model that explains how temperature gradients drive convective phase separation in attractive particle systems, revealing that the transition to periodic patterns is governed by a dominant unstable mode and results in robust steady-state convective currents.
This paper establishes a Newtonian-like framework for interacting spiral waves in excitable media, defining a time-varying "mass" and collision-based forces that govern their drift and complex N-body dynamics, with significant implications for understanding cardiac fibrillation.
This paper presents a theoretical framework demonstrating that hexagonal multiferroic media support electrically tunable nonlinear magnetoelastic solitons and breathers, where strong magnon-phonon hybridization leads to coherent, bounded dynamics rather than chaos, enabling precise control over soliton properties via external electric fields.