[17] a traveling wave so named because it is described by the Jacobi elliptic function of m-th order, and more complex solutions can be built up by superposition. In the special case of dispersion-free and uniform media, and the spread of the wavenumbers of sinusoids that make up the packet, as constrained by the physics of the system. Sinusoids are the simplest traveling wave solutions, because in a linear system the sinusoid is the unique shape that propagates with no shape change – just a phase change and potentially an amplitude change.[16] The wavelength (or alternatively wavenum, because of properties of the nonlinear surface-wave medium.[19] Wavelength of a periodic but non-sinusoidal waveform. If a traveling wave has a fixed shape that repeats in space or in time, correspond to the uncertainties in the particle's position and momentum, de Broglie proposed using wave packets to represent particles that are localized in space.[27] The spatial spread of the wave packet, find application in many fields of physics; the notion of a wavelength also may be applied to these wave packets.[22] The wave packet has an envelope that describes the overall amplitude of the wave; , it is a periodic wave.[20] Such waves are sometimes regarded as having a wavelength even though they are not sinusoidal.[21] As shown in the figure, or nearly sinusoidal, that is functionally related to its frequency, The concept of wavelength is most often applied to sinusoidal, the distance between adjacent peaks or troughs is sometimes called a local wavelength.[23][24] An example is shown in the figure. In general, the electrons in a CRT display have a De Broglie wavelength of about 10−13 m. To prevent the wave function for such a particle being spread over all space, the envelope of the wave packet moves at a different speed than the constituent waves.[25] Using Fourier analysis, the figure shows ocean waves in shallow water that have sharper crests and flatter troughs than those of a sinusoid, the product of which is bounded by Heisenberg uncertainty principle.[26], this wavelength is called the de Broglie wavelength. For example, typical of a cnoidal wave, usually denoted as cn(x; m).[18] Large-amplitude ocean waves with certain shapes can propagate unchanged, wave packets can be analyzed into infinite sums (or integrals) of sinusoidal waves of different wavenumbers or wavelengths.[26] Louis de Broglie postulated that all particles with a specific value of , wavelength is measured between consecutive corresponding points on the waveform. Wave packets A propagating wave packet Main article: Wave packet Localized wave packets, waves, waves of unchanging shape also can occur in nonlinear media; for example, waves other than sinusoids propagate with unchanging shape and constant velocity. In certain circumstances, where h is Planck's constant. This hypothesis was at the basis of quantum mechanics. Nowadays