Science AI Journal
Physics and Astronomy · Research topic

Open research questions in Nonlinear Waves and Solitons

235 gap statements mined from Nonlinear Waves and Solitons papers in our 7.9M-paper local library, which holds 2,819 papers on the topic — drawn mostly from each paper's own stated research gap, future-work, challenge and limitation notes, and its abstract. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one.

Choosing where to publish on Nonlinear Waves and Solitons? See the ranked Physics journals.

What the literature leaves open

  • The conventional diagnostics of quantum chaos based on spectral correlations of the Hamiltonian cannot be directly applied to supersymmetric black holes. There is a need for a new framework to diagnose chaos within the BPS subspace. The paper identifies a gap in understanding how the chaos-integrability transition occurs within the BPS subspace of a supersymmetric model.

    Chaos-integrability transition in the BPS subspace of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> SYK model · 2026 · DOI

  • The mechanical behavior of granular media is challenging to model due to its extreme nonlinearity and solid-and fluid-like properties. There is a need for a comprehensive understanding of the nonlinear behavior of sand ripples.

    Analytical solutions and artificial neural network approximations for sand ripples in granular media · 2026 · DOI

  • It needs to characterize the solutions of the obtained ordinary differential equations that correspond to the isoperiodic deformations. The study must apply these results to the theory of genus one solutions to the Boussinesq equation.

    Isoperiodic Deformations of Abelian Differentials of the Second Kind Over Elliptic Curves and the Boussinesq Equation · 2026 · DOI

  • The need to generalize the method to velocity-dependent forces and configuration space with curvature. The challenge of obtaining a nonperturbative description of the stability properties for a broad class of nonlinear systems.

    Nonlinear dynamics of rapidly driven systems · 2026 · DOI

  • The lack of a systematic method for including high-order and nonlinear effects in the theoretical description of rapidly driven systems. The limitation of most applications to the leading order linearized approximation, which reduces to the well-established theory of the Mathieu equation.

    Nonlinear dynamics of rapidly driven systems · 2026 · DOI

  • Nonlinear viscoelastic materials with frequency-dependent elastic constants are not well understood. There is a need for a model that accounts for both linear and nonlinear dissipation.

    Slowly decaying strain solitons in nonlinear viscoelastic waveguides · 2025 · DOI

  • There is a lack of new exact solutions to the gas dynamics equations. The existing solutions do not fully describe the motion of particles in gas dynamics.

    Partially invariant solution with an arbitrary surface of blow-up for the gas dynamics equations admitting pressure translation · 2024 · DOI

  • The freedom to realise special-function dynamics within integrable Kummer-type Hamiltonian systems remains underexplored.

    Generating integrable systems from an autonomous ordinary differential equation · 2026

  • The (2+1)-dimensional BKP equation is a new model that has not been extensively studied. There is a need for new methods to find exact solutions to nonlinear partial differential equations.

    Exact solutions for a (2+1)-dimensional B-type Kadomtsev-Petviashvili equation · 2026 · DOI

  • The linearization of third-order nonlinear ordinary differential equations is a challenging task. The method needs to be able to handle nonlinear terms. The method needs to be able to provide exact analytical solutions.

    UTILIZING THE GENERALIZED SUNDMAN TRANSFORMATION TO LINEARIZE THIRD-ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS · 2026 · DOI

  • There is a need for efficient methods to solve Klein-Gordon and Sine-Gordon equations. The existing methods may not provide accurate numerical solutions for linear and nonlinear problems.

    Application of the Aboodh Adomian Decomposition Method to Klein-Gordon and Sine-Gordon Equations · 2026 · DOI

  • Nonlinear wave phenomena in quantum plasmas is one of the most important areas of research in contemporary physics, but it requires more advanced analytical tools. The (3 + 1)-dimensional extended quantum nonlinear Zakharov-Kuznetsov equation is a more complex level of plasma dynamics in three spatial dimensions and time, but its solutions are not well understood.

    Dynamical analysis and soliton solutions to (3+1)-dimensional extended quantum nonlinear Zakharov–Kuznetsov equation · 2026 · DOI

  • The lack of explicit solution formulas for nonlinear rational difference equations. The need for a systematic methodological framework for solving multidimensional nonlinear difference equations.

    Algebraic Reduction and Periodic Solvability in a Coupled Ternary Rational System · 2026 · DOI

  • For the (2+1)-dimensional NLS equation discussed in this paper, the stability of the lump solutions, as well as that of high-order lump patterns, remains an open problem.

    High-Order Line-Soliton Interactions and Anomalous Scattering of Lumps in a (2+1)-Dimensional Reverse Space–Time Nonlinear Schrödinger Equation · 2026 · DOI

  • The Darboux transformation method has not been fully explored for the (2+1)-dimensional Hirota's system. There is a need for a comprehensive analysis of the system's dynamical properties.

    Solitons and breathers for the (2+1)-dimensional Hirota’s system · 2026 · DOI

  • There is a lack of explicit quasi-periodic solutions for the GI equation. The previous methods have limitations in deriving solutions for the GI equation.

    Finite-Gap Integration of the Gerdjikov-Ivanov Equation: a Classical Method · 2026 · DOI

  • The paper aims to fill this gap by using two semi-analytical techniques, the ESEM and the.G0G0+G+A/-expansion method, alongside the numerical DTM to investigate the equation.

    Analytical and numerical solutions of the integrable Shynaray-IIA equation: solitary wave dynamics in fiber optics · 2026 · DOI

  • The paper suggests that future research directions include the application of the vector bilinear formulation to other integrable systems. The approach can be used to study the behavior of solitons in various physical systems, such as optical fibers and Bose-Einstein condensates.

    A Vector Bilinear Framework for Soliton Dynamics in Coupled Modified KdV Systems · 2026 · DOI

  • The gap is the lack of a compact and structurally consistent framework for analyzing multi-component soliton solutions.

    A Vector Bilinear Framework for Soliton Dynamics in Coupled Modified KdV Systems · 2026 · DOI

  • Ensuring that the denominators remain nonzero within the fractional domain. Analyzing the qualitative behavior of the solutions.

    Algebraic Reduction and Periodic Solvability in a Coupled Ternary Rational System · 2026 · DOI

  • Investigating the holographic interpretation of the chaos-integrability crossover, - Exploring the application of BPS chaos diagnostics to other supersymmetric holographic systems, - Studying the relation between chaos and black hole dynamics in more general settings, - Investigating the breakdown of the black-holelike chaotic description as the model approaches the integrable…

    Chaos-integrability transition in the BPS subspace of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> SYK model · 2026 · DOI

  • The paper identifies a gap in the study of isoperiodic deformations of Abelian differentials of the second kind over elliptic curves. It extends the existing idea of isoperiodic deformations to Abelian differentials of the second kind on elliptic curves.

    Isoperiodic Deformations of Abelian Differentials of the Second Kind Over Elliptic Curves and the Boussinesq Equation · 2026 · DOI

  • Further study of the properties of the solutions obtained. Application of the modified double sub-equation method to other nonlinear partial differential equations.

    Exact solutions for a (2+1)-dimensional B-type Kadomtsev-Petviashvili equation · 2026 · DOI

  • To apply the Aboodh-Adomian Decomposition Method to other partial differential equations. To compare the method with other existing methods. To extend the method to solve other problems in science and engineering.

    Application of the Aboodh Adomian Decomposition Method to Klein-Gordon and Sine-Gordon Equations · 2026 · DOI

  • Further study of the Darboux transformation method for other integrable systems. Investigation of the physical properties and dynamic behaviors of the breathers on the periodic background.

    Solitons and breathers for the (2+1)-dimensional Hirota’s system · 2026 · DOI

Most-cited papers in Nonlinear Waves and Solitons

Most recent work

Find a gap in your own Nonlinear Waves and Solitons sub-topic

This page shows what the Nonlinear Waves and Solitons literature already flags as unresolved. To narrow it to your specific question, search the Research Gap Finder: the search is free with a free account and lists the papers closest to your topic first. Unlocking that topic (50 credits, charged once) fills the comparison table from our 7.9M-paper local library and writes the gaps from its rows.

Open the Research Gap Finder →

Related topics in Physics and Astronomy

Galaxies: Formation, Evolution, Phenomena
834 open questions
Stellar, planetary, and galactic studies
789 open questions
Model Reduction and Neural Networks
704 open questions
Cosmology and Gravitation Theories
667 open questions
Astro and Planetary Science
425 open questions
Advanced Radiotherapy Techniques
423 open questions
Pulsars and Gravitational Waves Research
411 open questions
Ionosphere and magnetosphere dynamics
400 open questions
Open questions raised by papers listed on this page include: (1) There is a need for a new framework to diagnose chaos within the BPS subspace (“Chaos-integrability transition in the BPS subspace of the <mml:math…”, 2026); (2) There is a need for a comprehensive understanding of the nonlinear behavior of sand ripples (“Analytical solutions and artificial neural network approximations for sand…”, 2026); (3) The lack of a systematic method for including high-order and nonlinear effects in the theoretical description of rapidly driven systems (“Nonlinear dynamics of rapidly driven systems”, 2026); (4) There is a need for new methods to find exact solutions to nonlinear partial differential equations (“Exact solutions for a (2+1)-dimensional B-type Kadomtsev-Petviashvili equation”, 2026); (5) There is a need for efficient methods to solve Klein-Gordon and Sine-Gordon equations (“Application of the Aboodh Adomian Decomposition Method to Klein-Gordon and…”, 2026). 235 gap statements have been mined from Nonlinear Waves and Solitons papers in our 7.9M-paper local library, which holds 2,819 papers on the topic; the gaps come from whichever of those papers state one. They are mostly the research gaps the authors state and the papers' abstracts, plus future-work, limitations and challenges passages. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one, so you can read the original claim in context.

Tools for your next paper

Gaps & Literature SearchFind open questions in any field — 1,100,000+ open gaps mined from our own library.Pre-CheckIs your paper ready? Acceptance odds for top, mid and open/emerging journals, in seconds.Journal FinderA ranked shortlist of target journals from a 17,500-venue index.Duplicate Publication CheckerCheck for prior publication across 7 sources and our local library.Citation GeneratorFreeA DOI or title → APA, MLA, Vancouver, Chicago, BibTeX, RIS. No signup.Graphical Abstract MakerFreeTurn your findings into a colorblind-safe graphical abstract.

How Pre-Check worksHow AI Review works

Compare the category — Honest roundups of the AI research tools, ours listed alongside the alternatives.

Command palette

Jump anywhere, run any action.