Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Quadratic Equations in the Complex Number System01:29

Quadratic Equations in the Complex Number System

A quadratic equation in the form ax2+bx+c=0 can have solutions that vary in nature depending on the value of the discriminant, b2−4ac. In this expression, a is the coefficient of the quadratic term x2, b is the coefficient of the linear term x, and c is the constant term. When the discriminant is negative, the equation has no real number solutions. However, by introducing complex numbers through the imaginary unit i, defined by i=-1, these equations can still be solved.The square root of a...
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
Van der Waals Equation01:10

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
The Van der Waals Equation01:26

The Van der Waals Equation

The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...
Divergence and Curl of Electric Field01:25

Divergence and Curl of Electric Field

The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
Bessel Function of Order Zero01:20

Bessel Function of Order Zero

A common physical example of wave propagation with radial symmetry is the ripple formed when a stone is dropped into a still pond. The disturbance originates at a central point and travels outward as a circular wave. As the radius of the wavefront increases, the same initial energy is distributed along a progressively larger circumference. Consequently, the amplitude, or height, of the wave decreases with distance from the center. This decay behavior cannot be captured by simple sine or cosine...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Complementary prognostic value of hotspot-to-centroid distance (NHOCpeak) to SUVpeak in high-grade glioma.

Annals of nuclear medicine·2026
Same author

First Explore, Then Settle: A Theoretical Analysis of Evolvability as a Driver of Adaptation.

Bulletin of mathematical biology·2026
Same author

Geometric immunosuppression in CAR T-cell treatment: Insights from mathematical modeling.

Computers in biology and medicine·2025
Same author

Computational flow cytometry immunophenotyping at diagnosis is unable to predict relapse in childhood B-cell Acute Lymphoblastic Leukemia.

Computers in biology and medicine·2025
Same author

Mathematical Model of CAR T-Cell Therapy for a B-Cell Lymphoma Lymph Node.

Bulletin of mathematical biology·2025
Same author

Understanding the role of B cells in CAR T-cell therapy in leukemia through a mathematical model.

Chaos (Woodbury, N.Y.)·2024

Related Experiment Video

Updated: Jun 29, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Eigenvalue cutoff in the cubic-quintic nonlinear Schrödinger equation.

Vladyslav Prytula1, Vadym Vekslerchik, Víctor M Pérez-García

  • 1Departamento de Matemáticas, E.T.S. Ingenieros Industriales and Instituto de Matemática Aplicada a la Ciencia y la Ingeniería, Universidad de Castilla-La Mancha, Avenida Camilo José Cela 3, Ciudad Real, 13071 Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
PubMed
Summary

This study proves that localized solutions for the cubic-quintic nonlinear Schrödinger equation have a maximum eigenvalue. This finding, using theoretical methods, clarifies the behavior of these nonlinear systems.

Related Experiment Videos

Last Updated: Jun 29, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

  • Nonlinear dynamics
  • Mathematical physics
  • Quantum mechanics

Background:

  • The cubic-quintic nonlinear Schrödinger equation (CQNLSE) models various physical phenomena.
  • Localized stationary solutions are crucial for understanding system behavior.
  • Numerical evidence suggested an upper bound for solution eigenvalues, but theoretical proof was lacking.

Purpose of the Study:

  • To theoretically prove the existence of an upper cutoff value for eigenvalues of localized stationary solutions of the (2+1)-dimensional CQNLSE.
  • To provide a rigorous mathematical foundation for a previously observed numerical phenomenon.
  • To analyze the behavior of eigenstates in limiting cases.

Main Methods:

  • Application of Gagliardo-Nirenberg inequalities.
  • Utilization of Hölder inequalities.
  • Employment of Pohozaev identities for theoretical analysis.

Main Results:

  • Theoretical proof of an upper cutoff value for eigenvalues of localized stationary solutions in the CQNLSE.
  • Demonstration that eigenstates approach those of the cubic nonlinear Schrödinger equation as eigenvalues approach zero.

Conclusions:

  • The upper cutoff for eigenvalues is a fundamental property of localized solutions in the CQNLSE.
  • The theoretical framework established provides new insights into the behavior of nonlinear Schrödinger equations.
  • Understanding these eigenvalue properties is essential for predicting the stability and dynamics of nonlinear systems.