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On the dynamics and integrability of the Ziegler pendulum
We prove that the Ziegler pendulum—a double pendulum with a follower force—can be integrable, provided that the stiffness of the elastic spring...
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Chaos and integrability of relativistic homogeneous potentials in curved space
Relativistic Hamiltonian systems of n degrees of freedom in static curved spaces are considered. The source of space-time curvature is a scalar...
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Integrability and exact solutions of the (2+1)-dimensional variable coefficient Ito equation
This paper focuses on the study of the (2+1)-dimensional Ito equation with spatially variable coefficients. The Lax integrability of the equation is...
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Dynamics and integrability of the swinging Atwood machine generalisations
This paper studies the dynamics and integrability of two generalisations of a 3D Swinging Atwood’s Machine with additional Coulomb’s interactions and...
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On integrability of the segmented disc dynamo: the effect of mechanical friction
The segmented disc dynamos with or without friction are two basic models describing the self-excitation of a magnetic field, which are used to...
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Integrability, lump solutions, breather solutions and hybrid solutions for the (2+1)-dimensional variable coefficient Korteweg-de Vries equation
This paper focuses on the integrability and exact solutions of a (2+1)-dimensional variable coefficient Korteweg-de Vries equation. The bilinear...
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Painlevé integrability and superposition wave solutions of Whitham–Broer–Kaup equations
In this paper, the Painlevé integrability and superposition wave solutions of Whitham–Broer–Kaup (WBK) equations are studied, which can help us...
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Painlevé integrability and lump solutions for two extended (3 + 1)- and (2 + 1)-dimensional Kadomtsev–Petviashvili equations
The current work introduces two extended (3 + 1)- and (2 + 1)-dimensional Painlevé integrable Kadomtsev–Petviashvili (KP) equations. The...
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Characteristic of integrability of nonautonomous KP-modified KP equation and its qualitative studies: soliton, shock, periodic waves, breather, positons and soliton interactions
This article demonstrates the characteristic of integrability of the nonautonomous KP-mKP equation through Painlevé analysis, bilinear Bäcklund and...
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Integrability of a generalized (2+1)-dimensional soliton equation via Bell polynomials
In this paper, we focus on the integrability of a generalized (2+1)-dimensional equation with three arbitrary constants. By using Bell polynomials,...
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Painlevé integrability and multi-wave pattern for (2+1)-dimensional long wave–short wave resonance interaction system
In this article, Painlevé analysis is employed to test the integrability of (2+1)-dimensional long wave–short wave resonance interaction system using...
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Integrability, multi-solitons, breathers, lumps and wave interactions for generalized extended Kadomtsev–Petviashvili equation
In this paper, we take into consideration a general form of the extended Kadomtsev–Petviashvili equation, which has several applications in applied...
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The Geometric Framework—Results on Integrability
In this chapter, we will focus our attention on the solvability of a set of partial differential equations of the first order, or equivalently the...
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A (2+1)-dimensional combined KdV–mKdV equation: integrability, stability analysis and soliton solutions
In this study, the (2+1)-dimensional combined Korteweg–de Vries and modified Korteweg–de Vries equation has been considered for the first time....
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Non-integrability of a model of elastic dumbbell satellite
We study the integrability of a model of elastic satellite whose centre of mass moves in a circular Keplerian orbit around a gravity centre. The...
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Lax integrability and exact solutions of the generalized (3+1) dimensional Ito equation
This article introduces a generalized (3+1) dimensional integrable Ito equation based on relevant literatures. Firstly, the bilinear form of the...
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Integrability, modulational instability and mixed localized wave solutions for the generalized nonlinear Schrödinger equation
Under investigation in this paper is the generalized nonlinear Schrödinger (g-NLS) equation which has extensive applications in various physical...
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On the integrability of Hamiltonian 1:2:2 resonance
We study the integrability of the Hamiltonian normal form of 1:2:2 resonance. It is known that this normal form truncated to order three is...
