bluuebunny/crossref_metadata_2025_split huggingface dataset:
Conclusions and Coda
Authors: Holliday Peter J. 
Published: November 2024

Abstract
The conclusion and coda argue that historical subjects are favored by cultures that emphasize personal and dynastic power; that most of the preceding case studies represent scenes of warfare because such themes portray the patrons as heroic victors, and that the viewing of these monuments revivifies the memory of exceptional leaders and their achievements. They summarize the various techniques makers deploy to emphasize the veracity of their narratives and thereby enhance their commemorative and propagandistic functions. They examine the significance of physical form for historical representations, including materiality, formal composition, and style, and how they affect the viewer’s perception of the historical subject depicted and thereby affect their conduct. An examination of the “afterlives” of several works discussed in the preceding chapters demonstrates how changed contexts can change the meaning received from those works. Finally, the conclusion and coda consider how new media in the modern era have impacted the fortune of historical subjects in art.
Linear Dispersive Wave Equations
Authors: Carretero-González R. , Frantzeskakis D.J. , Kevrekidis P.G. 
Published: November 2024

Abstract
This chapter provides an introduction to notions and ideas that will be used throughout the book. The ultimate goal is a presentation of nonlinear dispersive wave models that will be analyzed in more detail in the next chapters. A key element of this chapter will be the Fourier transform, which will allow us to derive dispersion relations from linear equations, and vice versa. Nonlinearity will also be introduced, via a heuristic approach, relying on the fundamental effect of the phase-speed dependence on the field-amplitude (this dependence discriminates, in fact, linear and nonlinear waves). The final twist will be the combination of dispersion and nonlinearity, which, as we will see in the following chapters, will lead to a variety of nonlinear dispersive wave equations.
The Korteweg–de Vries (KdV) Equation
Authors: Carretero-González R. , Frantzeskakis D.J. , Kevrekidis P.G. 
Published: November 2024

Abstract
In this chapter we study the quintessential model for propagation of surface waves in a nonlinear medium: the Korteweg-de Vries (KdV) equation. Its wide applicability stems from the fact that the KdV is a prototypical (normal form) partial differential equation (PDE) that supports nonlinear waves. For instance, we will see how the KdV may be obtained from two very different (opposing) physical limits: (i) a chain of nonlinear springs and (ii) as a simplification of the shallow water waves. We also introduce the method of characteristics to solve for traveling waves in general PDEs. This leads to the study of wave breaking and shock waves. We will combine all these ingredients to understand the FPUT paradox where, against expectations, over observed timescales, a nonlinear chain of springs may not be capable of equidistributing energy along its normal modes. Finally, we will also introduce the concept of conservation laws.
From Boussinesq to KdV – Boussinesq Solitons as KdV Solitons
Authors: Carretero-González R. , Frantzeskakis D.J. , Kevrekidis P.G. 
Published: November 2024

Abstract
In this chapter we focus on the asymptotic reduction of the Boussinesq equation to the KdV equation. We show how the slow variables and the scales of the unknown fields involved in the problem are chosen. We will see that relevant choices stem from "first principles", such as the structure of the linear dispersion relation, and the balance between dispersion and nonlinear effects. In addition, we will go a step further: relying on the formal asymptotic connection between the Boussinesq and KdV equations, we will show that the soliton solution of the former is nothing but the small-amplitude limit of the latter. Finally, we will show how results pertaining to the 1D setting can be generalized to higher-dimensions. In particular, we will present the asymptotic reduction of the 2D Boussinesq equation to the Kadomtsev-Petviashvili (KP) equation, which is the higher-dimensional generalization of the KdV.
Bäcklund Transformation for the KdV
Authors: Carretero-González R. , Frantzeskakis D.J. , Kevrekidis P.G. 
Published: November 2024

Abstract
In this chapter we introduce a very useful transformation, the so-called Bäcklund transformation. The motivation stems from the observation that, if we are able to craft “special” transformations that relate different solutions to a given PDE, maybe we can use these transformations to obtain new (independent) solutions from a previously known solution. We start motivating this methodology with a simple introductory example in terms of the Laplace equation. Then, we introduce the Bäcklund transformation for the KdV that will enable us to obtain the most general soliton solution starting from the most trivial KdV solution, the zero solution! Finally, we adapt this methodology to circumvent the different integrations needed when "undoing" the transformations and will derive a remarkable algebraic equation relating three solutions of the KdV. This will allow us to take two independent solutions traveling at different speeds and construct the exact two-soliton solution describing their collision.
The Kadomtsev–Petviashvili Equation*
Authors: Carretero-González R. , Frantzeskakis D.J. , Kevrekidis P.G. 
Published: November 2024

Abstract
Motivated by the discussion on the transverse instability of line solitons of the Kadomtsev-Petviashvili (KP) equation of the previous chapter, we will take a closer look at this universal (2+1)-dimensional model. In particular, this chapter formally presents the KP equation and some of its variants, discusses some of its basic properties, and presents its most fundamental solutions, namely the line solitons and lumps. In addition, we discuss the very interesting and intricate interactions of line solitons, as well as the so-called finite-genus and quasi-periodic solutions of the KP-II version.
Additional Tools/Results for Klein–Gordon Equations
Authors: Carretero-González R. , Frantzeskakis D.J. , Kevrekidis P.G. 
Published: November 2024

Abstract
The real (field theoretic) nature of Klein-Gordon (KG) equations, as well as their apparent simplicity in their form as nonlinear variants of the wave equation, renders them suitable “playgrounds” for exploring a number of ideas in such settings. In this chapter, we give some examples of such tools that can be used effectively in media governed by KG equations to identify solitary waves such as the Bäcklund transforms, to characterize their interactions (such as the so-called Manton method) and collisions, and explore the role of perturbations in them, including in higher dimensional settings.
Klein–Gordon to NLS Connection – Breathers as NLS Solitons
Authors: Carretero-González R. , Frantzeskakis D.J. , Kevrekidis P.G. 
Published: November 2024

Abstract
In this chapter, we elucidate an interesting connection between two different solutions of quite different models: the breather solutions of the sine-Gordon (sG) and the bright soliton solutions of the nonlinear Schrödinger (NLS) equation. Thus, similarly to what was done in Chap. 5 to link Boussinesq solutions with KdV solitons using multiple scales expansions, we will employ a perturbative scheme to derive the NLS equation from the sG model in the case of weak nonlinearity. Generically, the study of modulated waveforms in weakly dispersive and weakly nonlinear settings gives rise to the NLS equation. In this chapter we will see that, indeed, starting from the sG equation we can derive a NLS equation, a fact that will allow us to connect sG breathers to NLS solitons.
Interlude: Numerical Considerations for Nonlinear Wave Equations
Authors: Carretero-González R. , Frantzeskakis D.J. , Kevrekidis P.G. 
Published: November 2024

Abstract
This chapter presents some basic numerical techniques based on finite difference discretizations to find steady states of PDEs and their corresponding stability spectra. The (spatial) discretization allows us to cast an approximation to the original PDE as a system of coupled ODEs, namely a dynamical lattice. Importantly, this allows us to write algebraic (nonlinear) equations for steady states that can be solved using Newton-type methods. In turn, the stability of these steady states can be determined by computing the corresponding stability eigenvalue spectrum. Finally, we describe marching methods to evolve in time initial configurations. All these techniques are showcased for kink solutions of the sine-Gordon model. The corresponding (steady state, stability, and evolution) codes will be implemented in Matlab and explained in detail so that you will be able to adjust them accordingly for other PDEs and lattices.
Numerical Techniques for NLS
Authors: Carretero-González R. , Frantzeskakis D.J. , Kevrekidis P.G. 
Published: November 2024

Abstract
In this chapter we revisit some basic numerical methods to find steady states and their corresponding stability and to follow the dynamical evolution for nonlinear waves. In particular, we expand on the presentation of Chap. 17 which focused on real-valued equations, and adapt the techniques to the NLS equation. To formulate the corresponding steady state, stability, and dynamics codes we will rely on discretizing space using basic finite differences. We will then use Newton’s method on the ensuing discretized space to numerically find steady states to a prescribed accuracy. The stability spectrum for steady states will then be obtained by numerically solving the corresponding linear eigenvalue problem on the discretized space. Finally, using standard Runge-Kutta time integration, we will follow the evolution dynamics for arbitrary initial configurations.
Variational Approximation for the NLS and GP Equations
Authors: Carretero-González R. , Frantzeskakis D.J. , Kevrekidis P.G. 
Published: November 2024

Abstract
In this chapter we present the variational approximation (VA) methodology to find approximate solutions of the NLS and GP PDEs. The VA method relies on projecting the dynamics on a suitable solution ansatz with time-dependent shape parameters. This allows to effectively reduce the infinite-dimensional evolution of the original PDE into a low-dimensional space spanned by the shape ansatz. This reduction typically yields a set of coupled ODEs for the shape parameters. We also show that by relying on perturbation theory within the VA approach, we are able to include correction terms in the dynamics that account for small perturbations of the original models. In particular, we deploy the VA methodology to describe the evolution of bright and dark solitons under confining potentials, the evolution of bright solitons under different types of loss mechanisms, and the mutual soliton interactions in the case of bright and dark solitons.
Transverse Instability of Solitons Stripes – Perturbative Approach
Authors: Carretero-González R. , Frantzeskakis D.J. , Kevrekidis P.G. 
Published: November 2024

Abstract
This chapter tackles one of the most important instabilities of NLS solitons: the transverse instability of a soliton stripe. The main question that we cover is whether these stripe (“ridge-like”) solutions are robust in 2D (or higher-dimensions)? In NLS and related models, the answer more often than not tends to be in the negative! Thus, exploring the resulting transverse instabilities is a topic of both time-honored history and particular practical interest, as these instabilities can be used to induce the controlled formation of a prescribed number of higher-dimensional coherent structures that spontaneously arise as a result of these instabilities, such as vortices. In particular, this chapter is devoted to the study of the transverse instability of NLS soliton stripes via a multiscale perturbative approach, similar to the one used in Chap. 12.
Vortices in the 2D Defocusing NLS
Authors: Carretero-González R. , Frantzeskakis D.J. , Kevrekidis P.G. 
Published: November 2024

Abstract
In this chapter we describe one of the most interesting and prevalent coherent structures that the NLS has to offer: the vortex solution. Owing to the tight connection between the NLS and a quantum superfluid (fluid without viscosity), vortices in the NLS have extraordinary properties. For instance, NLS vortices are quantized in their topological charge (angular momentum); unit charge vortices are structurally stable (they are very hard to destroy!), and their interaction dynamics can be reduced to an elegant Hamiltonian system of ODEs on the vortex positions corresponding to the celebrated point-vortex model.
The Discrete Klein–Gordon Model
Authors: Carretero-González R. , Frantzeskakis D.J. , Kevrekidis P.G. 
Published: November 2024

Abstract
In this chapter we explore the implications of discreteness on solitary waves in the discrete Klein-Gordon (KG) equations. We offer two complementary perspectives to the discreteness of the model: (i) the anti-continuum limit of vanishing coupling where the waveforms’ stability properties can be described and (ii) the near-continuum, energy-based one, showcasing the famous periodic Peierls-Nabarro barrier. The effects of discreteness prompt the question of whether certain “exceptional” discretizations of the underlying continuum problem may be able to restore the translational invariance that is normally broken by discreteness. We also briefly discuss an integrable discretization in the context of the sine-Gordon model which provides an opportunity to retrieve not just one but infinitely many conservation laws in line with the corresponding continuum model.
Discrete Models of the Nonlinear Schrödinger Type
Authors: Carretero-González R. , Frantzeskakis D.J. , Kevrekidis P.G. 
Published: November 2024

Abstract
This chapter is devoted to the study of the discrete NLS which is rather universal as a lattice nonlinear dispersive dynamical model. We start with the anti-continuum limit, near which a detailed analysis of the existence and stability of the emerging states is available. This view is complemented by a variational characterization of discrete solitary waves. We then provide a "teaser" regarding some of the exciting variations that higher dimensions bring about to the system. For instance, even the fundamental site-centered solitary wave is found to have a transition from stability to instability in higher dimensions, as its unstable continuum limit is approached. Moreover, a wide range of novel structures arise in such higher-dimensional realms in the form of vortical patterns whose existence and stability are also discussed. We also briefly discuss the particularly interesting variant of the integrable discrete NLS, in the form of the Ablowitz-Ladik model.
From Toda to FPUT and Beyond
Authors: Carretero-González R. , Frantzeskakis D.J. , Kevrekidis P.G. 
Published: November 2024

Abstract
Finally, in this chapter, we examine one of the arguably most famous integrable models in the form of the Toda lattice, along with its conservation laws and solitonic solutions. Then, coming in a sense full circle back to where we started, we reconnect the relevant systems to the Fermi-Pasta-Ulam-Tsingou (FPUT) class of models and take the opportunity to explore some of their corresponding features. More concretely, we examine the traveling wave coherent structures in a general form of such systems, but also give a concrete example of their experimental realization in the realm of the so-called granular crystals. We close with a more “forward-looking” direction giving a brief introduction into the far less studied shock wave patterns in discrete media and some pointers about future possibilities in this vein.
Costs
Authors: Sorabji John 
Published: November 2024

Abstract
The extent of litigation cost has been a continuing problem for English and Welsh civil procedure since the Middle Ages. It has been the cause of procedural reform at least once a decade since the 1820s. This Part sets out an approach to litigation cost that builds on the approach reached by the CPR following the introduction of expanded fixed recoverable costs. It rejects cost budgeting as a cost-effective and efficient means of controlling litigation cost, but provides for the general promotion of prospective costs control and for generally applicable fixed (tariff) costs, with the possibility of proportionate costs for those cases to which tariff costs do not apply. It also provides for oversight and regulation of litigation costs by a Costs and Funding Council, which provides a key link between these two key features of dispute resolution and provides for the regular revision of tariff and proportionate costs.
Funding
Authors: Sorabji John 
Published: November 2024

Abstract
Civil procedure codes do not ordinarily make provision for litigation funding. This Part, which should be read with Part 3 on Costs, details a potential litigation funding regime, the aim of which is to ensure universal provision of necessary litigation funding. The funding regime should be co-ordinated with the promotion of preventive and consensual dispute resolution and not simply with access to court adjudication. It should also promote a variety of different means through which funding can be secured. The primary route to funding is the promotion of mandatory legal expenses insurance, consequent on the introduction of tariff costs in Part 3, as the generally applicable form of litigation funding for individuals. Funding premiums are to be paid by the State for those individuals who are in receipt of welfare benefits. Legal aid becomes a residuary form of funding. Other private forms of funding it promotes are a general form of contingent fee agreement, which replaces CFAs and DBAs, and third-party litigation funding.
Amendment
Authors: Sorabji John 
Published: November 2024

Abstract
Case statements may require amendment during the course of litigation. They may contain errors. They may need revision in the light of new information or evidence. They may also require amendment following, for instance, successful applications to strike out aspects of a party’s pleaded case. This Part sets out a codification of the rules concerning amendment. It makes provision for the general approach to amendment both for case statements and other procedural documents. It makes provision for a stricter approach, consistent with the CPR, to late amendments. It also codifies in a single place rules concerning amendment to change the capacity in which a party brings or defends a claim and those to add, remove or substitute a party to proceedings both before and after the expiry of a relevant statutory limitation period.
Service
Authors: Sorabji John 
Published: November 2024

Abstract
Service of case statements and other procedural documents is an essential means by which the court’s jurisdiction over parties is established and by which parties are given effective notice of proceedings. This Part provides a simple service process, primarily to be carried out by the court through an effective digital case management system. Consistently with the emphasis on digital service, it gives precedent to forms of service effected via electronic (digital) means, whether email, text, social media, or otherwise. The key test for permitting the use of electronic service methods is whether they are reasonably likely to bring service to the attention of the party being served. Party consent to use an electronic method is not required. Non-electronic methods of service remain capable of use in the alternative. Provisions concerned service out of the jurisdiction, deemed service, dispensing with service, and time limits for service are also set out.
Access to Evidence and Privileges
Authors: Sorabji John 
Published: November 2024

Abstract
Party and court access to evidence is essential for the identification of right fact in adjudication. It is also essential for parties engaged in attempts to settle their dispute consensually. This Part makes provision for access to witness evidence, documentary evidence, and expert evidence (including court-appointed experts). It also codifies the burden and standard of proof and evidentiary privileges. It introduces specific rules permitting, in limited circumstances, the court to assist parties who are not represented by lawyers to identify evidence they may wish to adduce. It also makes provision for legal professional privilege, revises the privilege against self-incrimination so that it is a ‘use immunity’, and introduces a general form of settlement privilege. While it provides an illustrative rule concerning closed material proceedings, this Part rejects the incorporation of such a form of process as being inimical to the right to fair trial.
Provisional Measures
Authors: Sorabji John 
Published: November 2024

Abstract
The effective administration of justice may require the court to grant a range of provisional measures. Such measures have, historically, not been systemised in England and Wales, although they have in other jurisdictions. This Part provides a functional systemisation of those provisional measures available to support litigation in England and Wales. It characterises the various measures as either: preservative; regulatory; or anticipatory. Civil Search Orders and freezing injunctions, for instance, act as preservative measures. Interim injunctions and interim declarations are regulatory in nature. Interim payment orders are anticipatory. The criteria governing the grant of each type of measure is also codified.
Prelude
Authors: Simpson Barbara 
Published: November 2024

Abstract
The Prelude sets out the stall upon which this book is constructed. It presents an argument that the purpose of leadership is distinct from that of management, and therefore these two concepts need to be theorised and researched differently. Focussing specifically on leadership, it suggests this complex phenomenon may be differently understood in terms of the two complementary aspects of the ‘leader’/‘leading’ duality, where the former aspect is based on a substantive ontology and the latter on a processual ontology. Pragmatism, as a philosophy of process, is introduced as a diffractive apparatus that is consistent with such a processual ontology. The structure of the book is then outlined, drawing on music and the modernist literature of writers such as Virginia Woolf as guiding metaphors.
First Movement
Authors: Simpson Barbara 
Published: November 2024

Abstract
This movement is comprised of an Intermezzo that examines Pragmatist thinking on community and democracy, and an Étude that exemplifies the culture of collaboration in the senior management team of an arts-based company. The Intermezzo draws primarily on the writing of Jane Addams, but also includes contributions from John Dewey, George Herbert Mead, and Mary Parker Follett. The Étude contrasts this Pragmatist view with familiar critiques of committees and committee work in organizations. It also sets the scene for the empirical study that runs throughout this book, which is based on the collaborative efforts of a diverse team of managers.
Reading
Authors: Russell David 
Published: November 2024

Abstract
This chapter examines Milner’s diary books of the 1930s – A Life of One’s Own and an Experiment in Leisure – in order to define the terms of her lifelong quest for a creative life. It explores the ways Milner finds her own relationship to language, and to her reading, in order to open paths to creativity. In particular it analyses Milner’s invention of a ‘meta-diary’ practice – a writing of essays which reflect on past diaries – in order to show how Milner engages with language as a medium for finding the life she wants. The chapter contextualises Milner’s writing in relation to the essayists of the nineteenth century, and the Bloomsbury and modernist novelists of the twentieth century. It also looks ahead to the question of how Milner’s thinking about her own art and interests will shape a therapeutic practice.